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  • Articles  (263)
  • Articles: DFG German National Licenses  (263)
  • Mathematics and Statistics  (263)
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  • Mathematics  (263)
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  • Articles  (263)
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  • Articles: DFG German National Licenses  (263)
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  • Mathematics  (263)
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  • 1
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    Vacuum and non-vacuum solutions of the quasi-hydrodynamic semiconductor model in thermal equilibrium (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 225-254 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The quasi-hydrodynamical model for bipolar semiconductor devices in thermal equilibrium admits in general solutions for which the non-negative electron- or hole-density is not strict positive. In this paper sufficient conditions depending on the device's data which lead to or prevent vacuum are presented. The transformation of the model equations to a single semilinear elliptic mixed boundary value problem for the electrostatic potential V reduces the vacuum-non-vacuum discussion to an investigation of the range of V. Monotonicity arguments and the employment of local sub- and supersolutions allow to estimate the size as well as the distance from the Dirichlet boundary of the respective vacuum sets. An one-dimensional model is analysed in some detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670180304
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  • 2
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    Global existence and blow-up for a system of heat equations with non-linear boundary conditions (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 307-315 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, we consider non-negative solutions of We prove that if pq ≤ 1 every solution remains bounded, while all solutions blow up in a finite time if pq 〉 1. We also show that if p,q 〉 1, then blow-up can only occur on the boundary.
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    URL: http://dx.doi.org/10.1002/mma.1670180405
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  • 3
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    On the sharp singular limit for slightly compressible fluids (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 295-306 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the equations of motion to slightly compressible fluids and we prove that solutions converge, in the strong norm, to the solution of the equations of motion of incompressible fluids, as the Mach number goes to zero. From a physical point of view this means the following. Assume that we are dealing with a well-specified fluid, so slightly compressible that we assume it to be incompressible. Our result means that the distance between the (continuous) trajectories of the real and of the idealized solution is ‘small’ with respect to the natural metric, i.e. the metric that endows the data space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670180404
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  • 4
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    Boundary layer resolution in hierarchical plate modelling (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 345-370 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The dimensional reduction of an elliptic model boundary value problem on a thin, plate-like domain of thickness 2d is analysed. A class of lower-dimensional models with variable model orders in the interior and near the boundary of the plate is investigated and it is shown that for a sufficiently large model order in a O(d∣ln d∣)-neighbourhood of the edge the hierarchical models compensate for the boundary layers of the exact solution - in the sense that their asymptotic rate of convergence as d → 0 is the same as the optimal one for compatible, layer-free solutions.
    Additional Material: 1 Tab.
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    URL: http://dx.doi.org/10.1002/mma.1670180503
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  • 5
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    Similarity solutions of dispersive long-wave equations in two space dimensions (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 789-802 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, both the direct method and the non-classical Lie approach are applied to reduce the (2 + 1)-dimensional dispersive long wave equations. Nine types of two-dimensional PDE reductions and 13 types of ODE reductions are given. All the known reductions obtained by the classical Lie approach are reobtained as some special cases. Similar to the (1 + 1)-dimensional case, some types of reductions with essential and logarithmic singular characteristic manifolds are allowed although the model is integrable.
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    URL: http://dx.doi.org/10.1002/mma.1670181004
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  • 6
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    On the initial value problem for the Vlasov-Poisson-Fokker-Planck system with initial data in Lp spaces (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 825-839 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper the global existence of weak solutions for the Vlasov-Poisson-Fokker-Planck equations in three dimensions is proved with an L1 ∩ Lp initial data. Also, the global existence of weak solutions in four dimensions with small initial data is studied. A convergence of the solutions is obtained to those built by E. Horst and R. Hunze when the Fokker-Planck term vanishes. In order to obtain the a priori necessary estimates a sequence of approximate problems is introduced. This sequence is obtained starting from a non-linear regulation of the problem together with a linearization via a time retarded mollification of the non-linear term. The a priori bounds are reached by means of the control of the kinetic energy in the approximate sequence of problems. Then, the proof is completed obtaining the equicontinuity properties which allow to pass to the limit.
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    URL: http://dx.doi.org/10.1002/mma.1670181006
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  • 7
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    An explicit solution of the pseudo-hyperbolic initial boundary value problem in a multiply connected region (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 897-925 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An explicit solution of the pseudo-hyperbolic initial boundary value problem with a mixed boundary condition has been constructed. The problem describes the propagation of non-stationary internal waves in a stratified and rotational fluid. The generation of waves is caused by small oscillations of double-sided plates beginning at time t = 0. Dynamic pressure is specified on one set of plates and this yields the first boundary condition. Normal velocities are specified on another set of plates and this leads to an analogue of the second boundary condition with time derivatives. The solution has been obtained by the method of non-classical time-dependent dynamic potentials. The uniqueness of the solution has been studied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670181105
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  • 8
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    A discrete velocity coagulation-fragmentation model (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 959-993 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A discrete velocity Boltzmann model is introduced. It is based on two principles: (i) clusters of particles move in a volume V with seven fixed momenta; (ii) clusters may gain or lose particles according to the rules of Becker-Döring cluster equations. The model provides a kinetic representation of evaporation and condensation. Results of numerical experiments are presented.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670181204
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  • 9
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    On a local in time solvability of the Neumann problem of quasilinear hyperbolic parabolic coupled systems (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1053-1082 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove a local in time existence theorem of classical solutions to some coupled system of quasilinear hyperbolic equations and quasilinear parabolic equations with Neumann boundary condition. This coupled system contains a non-linear thermoelastic equation as an important physical example.
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    URL: http://dx.doi.org/10.1002/mma.1670181304
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  • 10
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    On the one- and one-half-dimensional relativistic Vlasov-Fokker-Planck-Maxwell system (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1013-1040 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, we study the relativistic Vlasov-Fokker-Planck-Maxwell system in one space variable and two momentum variables. This non-linear system of equations consists of a transport equation for the phase space distribution function combined with Maxwell's equations for the electric and magnetic fields. It is important in modelling distribution of charged particles in the kinetic theory of plasma. We prove the existence of a classical solution when the initial density decays fast enough with respect to the momentum variables. The solution which shares this same decay condition along with its first derivatives in the momentum variables is unique.
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    URL: http://dx.doi.org/10.1002/mma.1670181302
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  • 11
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    A particle method for a self-gravitating fluid: A convergence result (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1083-1094 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study an Hamiltonian system of N particles in ∝3 interacting by a short-range repulsive and a long-range attractive potential. It is shown that the empirical measures associated to the positions and velocity of the system converge to the solutions of Euler equations for a self-gravitating fluid, in the limit as the particle number tends to infinity, for a suitable scaling of the interactions.
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    URL: http://dx.doi.org/10.1002/mma.1670181305
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  • 12
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    Periodic optimal control for parabolic Volterra-Lotka type equations (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 127-146 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper considers the optimal harvesting control of a biological species, whose growth is governed by the parabolic diffusive Volterra-Lotka equation. We prove that such equation with L∞ periodic coefficients has an unique positive periodic solution. We show the existence and uniqueness of an optimal control, and under certain conditions, we characterize the optimal control in terms of a parabolic optimality system. A monotone sequence which converges to the optimal control is constructed.
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    URL: http://dx.doi.org/10.1002/mma.1670180204
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  • 13
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    Asymptotic characterization of standing waves and of the static limit for a class of wave equations of higher order with a variable coefficient and time-independent incitation (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 147-168 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the equation (-1)m∇m (p∇mu) + ∂t2u = ƒ in ∝n × (0, ∞) for arbitrary positive integers m and n and under the assumptions p - 1, ƒ ∊ C0∞(∝n) and p 〉 0. Even if the differential operator (-1)m∇m (p∇mu) has no eigenvalues, the solution u(x,t) may increase as t → ∞ for 2m ≥ n. For this case, we derive necessary and sufficient conditions for the convergence of u(x,t) as t → ∞. Furthermore, we characterize the functions occurring in these conditions as solutions of the homogeneous static equation (-1)m∇m (p∇mu) = 0, which satisfy appropriate asymptotic conditions at infinity. We also give an asymptotic characterization of the static limit.
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    URL: http://dx.doi.org/10.1002/mma.1670180205
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  • 14
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    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670180401
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  • 15
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    Existence of a solution for a lubrication problem in elastic journal-bearing devices with thin bearing (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 255-266 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A particular elastohydrodynamic lubrication problem is modelled in this work. The presence of elasticity, lubrication and cavitation calls for a non-linear coupled system of variational equations. The existence of a solution is deduced by means of a constructive algorithm that decouples biharmonic equation of the elastic hinged plate and the lubrication-cavitation Elrod-Adams free boundary problem.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670180402
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  • 16
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    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670180501
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  • 17
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    On the bending of plates with transverse shear deformation and mixed periodic boundary conditions (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 337-344 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The method of matched asymptotic expansions is used to find a homogenized problem whose solution is an approximation to the solution of a mixed periodic boundary value problem in the theory of bending of thin elastic plates. A critical size for the fixed parts of the boundary is found such that the boundary condition of the homogenized problem is an intermediate case between that for the clamped edge plate and that for the free boundary plate.
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    URL: http://dx.doi.org/10.1002/mma.1670180502
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  • 18
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    The free boundary problem of a semiconductor in thermal equilibrium (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 387-412 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The quasi-hydrodynamic model for semiconductor devices in thermal equilibrium admits in general solutions for which the electron or hole density vanish. These sets are called vacuum sets. In this paper estimates on the vacuum sets and a first step in the regularity of the free boundary of these sets are presented. Numerical examples, including error estimates for linear finite elements, for the devices diode, bipolar transistor and thyristor indicate that the free boundary is more regular than theoretically predicted.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670180505
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  • 19
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    Thermal deformations of inhomogeneous elastic plates (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 423-436 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider thermal deformations of transversally inhomogenous elastic plates. Thin plate equations are derived as limits of full three-dimensional models both in the linear as well as in the non-linear case with appropriate convergence proofs. In the non-linear case also the corresponding von Kármán equations are formulated. It is obtained that the inhomogeneity leads to the loss of some symmetry properties at the von Kármán equations.
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    URL: http://dx.doi.org/10.1002/mma.1670180602
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  • 20
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    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670180701
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  • 21
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    The double layer potential method for a boundary transmission problem for the Laplace operator in an infinite wedge (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 515-528 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper is concerned with the solution of a boundary transmission problem in an infinite wedge. We treat this problem by a boundary integral method using Green's contact function for two half-spaces. The integral operators are studied via a harmonic analysis approach which goes back to a paper of Fabes et al. We improve their results studying the Fourier symbol of the associated integral operators on the half-plane. This leads to invertibility criteria for the boundary integral operators.
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    URL: http://dx.doi.org/10.1002/mma.1670180703
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  • 22
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    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670180801
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  • 23
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    About the concept of measure-valued solutions to distributed parameter systems (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 671-685 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The measure-valued (mv) solutions are commonly defined in the literature simply by putting Young measures into the respective partial differential equations. Here a few examples of mv-solutions to evolution problems (conservation laws, fluid dynamics and a so-called backward-forward heat problem) are re-investigated to show that such definitions are not satisfactorily selective, i.e. they admit (sometimes surprisingly) many mv-solutions apparently without any physical sense. Then an attempt for a selective definition in the case of the backward-forward heat problem is made, resulting to a certain evolution variational inequality.
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    URL: http://dx.doi.org/10.1002/mma.1670180902
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  • 24
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    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670181001
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  • 25
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    A new system of boundary integral equations for plates with free edges (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 755-772 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present a new system of boundary integral equations for the free-edge plate. This system expresses an abstract symmetric variational problem posed on the boundary of the plate. In order to obtain this abstract problem, we must set the exterior boundary value problem corresponding to the free-edge plate in a framework of weighted Sobolev spaces. Finally, we take care of the hypersingular kernels appearing in our system of BIEs, by using an abstract technique of integration by parts.
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    URL: http://dx.doi.org/10.1002/mma.1670181002
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  • 26
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    The sorption of mixtures under linear equilibrium partitioning and chemical transformation (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 803-823 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the flow of a mixture, whose components are undergoing temporally and spatially varying linear equilibrium sorption partitioning and, possibly nonlinear, chemical transformations. We are able to generate an evolution system of parabolic type on the space of uniformly continuous functions and thus obtain classical solutions for arbitrary initial values.
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    URL: http://dx.doi.org/10.1002/mma.1670181005
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  • 27
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    Large time asymptotics for a class of wave equations of higher order with a variable coefficient and time-independent incitation (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1-25 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the equation (-1)m∇m (p∇mu) + ∂t2u = ƒ in ∝n × [0, ∞] for arbitrary positive integers m and n and under the assumptions p -1, ƒ ∊ C0∞ and p 〉 0. Under the additional assumption that the differential operator (-1)m∇m (p∇mu) has no eigenvalues we derive an asymptotic expansion for u(x,t) as t → including all terms up to order o(1). In particular, we show that for 2m ≥ n terms of the orders tα, log t, (log t)2 and tβ·log t as t → ∞ may occur.
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  • 28
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    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670180201
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  • 29
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    Non-orthogonal expansions on the sphere (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 83-120 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Discrete families of functions with the property that every function in a certain space can be represented by its formal Fourier series expansion are developed on the sphere. A Fourier-series-type expansion is obviously true if the family is an orthonormal basis of a Hilbert space, but it also can hold in situations where the family is not orthogonal and is ‘overcomplete’. Furthermore, all functions in our approach are axisymmetric (depending only on the spherical distance) so that they can be used adequately in (rotation) invariant pseudo-differential equations on the sphere. The three classes of examples particularly studied here are (i) Abel-Poisson frames (ii) Gauss-Weierstrass frames and (iii) frames consisting of locally supported kernel functions. Abel-Poisson frames form families of harmonic functions and provide us with powerful approximation tools in potential theory. Gauss-Weierstrass frames are intimately related to the diffusion equation on the sphere and play an important role in multiscale descriptions of image processing on the sphere. The third class enables us to discuss spherical ‘Fourier expansions’ by means of ‘axisymmetric finite elements’.
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    Local existence of solutions of impedance initial-boundary value problem for non-linear Maxwell equations (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 169-199 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Local existence of solutions of a mixed problem for non-linear Maxwell equations is proved. The solution is so regular that its third derivatives are from L2. However, the considered problem is characteristic we were able to obtain necessary estimate because compatibility conditions were used.
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    Inverse scattering from an open arc (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 267-293 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A Newton method is presented for the approximate solution of the inverse problem to determine the shape of a sound-soft or perfectly conducting arc from a knowledge of the far-field pattern for the scattering of time-harmonic plane waves. Fréchet differentiability with respect to the boundary is shown for the far-field operator, which for a fixed incident wave maps the boundary arc onto the far-field pattern of the scattered wave. For the sake of completeness, the first part of the paper gives a short outline on the corresponding direct problem via an integral equation method including the numerical solution.
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    Global solutions for operator Riccati equations with unbounded coefficients: A non-linear semigroup approach (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 317-336 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Let X be a Banach space of real-valued functions on [0, 1] and let ℒ(X) be the space of bounded linear operators on X. We are interested in solutions R:(0, ∞) → ℒ(X) for the operator Riccati equation \documentclass{article}\pagestyle{empty}\begin{document}$$ R′ + TR + RT = TB_1 (t) + TB_2 (t)R + RTB_3 (t) + RTB_4 (t)R, $$\end{document} where T is an unbounded multiplication operator in X and the Bi(t)'s are bounded linear integral operators on X. This equation arises in transport theory as the result of an invariant embedding of the Boltzmann equation. Solutions which are of physical interest are those that take on values in the space of bounded linear operators on L1(0, 1). Conditions on X, R(0), T, and the coefficients are found such that the theory of non-linear semigroups may be used to prove global existence of strong solutions in ℒ(X) that also satisfy R(t) ∊ ℒ(L1(0,1)) for all t ≥ 0.
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    Masthead (1995)
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    Mathematical Methods in the Applied Sciences 18 (1995) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Remark on a trace theorem for transmission problems (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 413-421 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In this paper we discuss elliptic transmission problems of second order in plane non-smooth domains with non-homogeneous boundary data. It is known that if the boundary data are homogeneous, then the variational solution of the transmission problem admits a representation as a sum of a regular function and certain singular functions, analogous to that encountered in boundary value problems on corner domains. We determine for which domains arbitrary non-homogeneous boundary data can be reduced to the homogeneous ones preserving availability of the representation formula. In the remaining cases we find the compatibility conditions for the data which also yield such a reduction.
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    Averaging in non-linear advective transport problems (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 437-448 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: Advective transport in a tidal basin is modelled by a non-linear parabolic equation with initial-boundary values. The model includes small effects such as diffusion, the reststream, reaction effects and sources. For a given periodic flow field, the long-time behaviour of the solutions is approximated by using the averaging method. We show the existence of a periodic solution and we demonstrate the asymptotic validity of the approximations for all time using maximum principles.
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    A generalization of the H-theorem to steady non-equilibrium states. Part 1: A basic decomposition and the linear case (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 507-513 
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    Notes: A generalized relative entropy functional is associated to the evolution of gas in a container with (generally) non-uniform boundary data. A decomposition for its rate in ‘bulk’ and in ‘boundary’ terms is given; for the linear case both have a definite sign. The relation with the strong L1 stability is pointed out.
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    Stability of semilinear ill-posed problems with a prescribed energy bound (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 549-569 
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    Notes: In the present paper we discuss the stability of semilinear problems of the form Aαu + Gα(u) = ƒ under assumption of an a priori bound for an energy functional Eα(u) ≤ E, where α is a parameter in a metric space M. Following [11] the problem Aαu + Gα(u) = ƒ, Eα(u) ≤ E is called stable in a Hilbert space H at a point α ∊ M if for any ƒ∊H, E, ∊ 〉 0 there exists δ 〉 0 such that for any functions uα1, uα2 satisfying Aαjuαj + Gαj(uαj) = ƒαj, Eαj(uαj) ≤ E, j = 1,2 we have ‖uα1 - uα2H ≤ ∊ provided ρM(αj, α) ≤ δ, ‖ƒαj - ƒ‖H ≤ δ, j = 1,2. In the present paper we obtain stability conditions for the problem Aαu + Gα(u) = ƒ, Eα(u) ≤ E.
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    Convergence of alternating domain decomposition schemes for kinetic and aerodynamic equations (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 649-670 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: A domain decomposition scheme linking linearized kinetic and aerodynamic equations is considered. Convergence of the alternating scheme is shown. Moreover the physical correctness of the obtained coupled solutions is discussed.
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    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Quaternionic representation of the 3D elastic and thermoelastic boundary problems (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 697-708 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: This paper contains new representations of the 3D elasticity and thermoelasticity problems, expressed in terms of regular quaternion functions, which in 3D and 4D have properties analogous to those of complex analytical functions in 2D. The known and some new results, described in the paper, are used to formulate boundary 3D problems, related to the theory. The formulae obtained are very similar to those given by Muskhelishvili for 2D boundary problems. The obtained representations can be used for development of a 3D boundary element method in numerical analysis.
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    Calculation of microstrains and microstresses in a thick non-symmetric heterogeneous plate by homogenization (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 723-737 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We consider the thermoelastic behaviour of a thick heterogeneous plate containing in its thickness a large number of periodically distributed transverse holes or inclusions. We use the Reissner-Mindlin thermoelastic linear model of thick plates with a known temperature and we distinguish displacements in the upper and lower part of the plate with respect to the middle plane. Due to the structure of the plate, thermal and elastic coefficients are non-uniformly and rapidly oscillating functions of the space variable. Two-scale convergence, which is the state of the art in mathematical homogenization technics, is used and gives convergence results and formulae allowing to calculate the distribution of microstrains and microstresses inside the plate when a macroscopic behaviour is given.
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    Global wellposedness for quasi-linear symmetric hyperbolic systems with regularized coefficients (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 773-787 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: Following the abstract setting of [8] and using the global results of [2], global wellposedness and regularity results are proved for the solutions of quasi-linear symmetric hyperbolic systems with bounded coefficients which are regularized by a convolution in the space variables with a regularizing function. In the case of unbounded regularized coefficients, local existence of classical solutions is proved, as well as uniqueness and regularity of (not necessarily existing) global weak solutions with initial value in a Sobolev space. As the regularizing function tends to Dirac's δ, local-in-time convergence to the classical solution of the non-regularized problem is proved.
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    Masthead (1995)
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    Mathematical Methods in the Applied Sciences 18 (1995) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Masthead (1995)
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    Mathematical Methods in the Applied Sciences 18 (1995) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    On the stationary quasi-Newtonian flow obeying a power-law (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 927-948 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: We investigate in this paper existence of a weak solution for a stationary incompressible Navier-Stokes system with non-linear viscosity and with non-homogeneous boundary conditions for velocity on the boundary. Our concern is with the viscosity obeying the power-law dependence ν(ξ) = ∣Tr(ξξ*)∣r/2-1, r 〈 2, on shear stress ξ. It is corresponding to most quasi-Newtonian flows with injection on the boundary. Since for r ≤ 2 the inertial term precludes any a priori estimate in general, we suppose the Reynolds number is not too large. Using the specific algebraic structure of the Navier-Stokes system we prove existence of at least one approximate solution. The constructed approximate solution turns out to be uniformly bounded in W1,r (Omega;)n and using monotonicity and compactness we successfully pass to the limit for r ≥ 3n/(n + 2). For 3n/(n + 2) 〉 r 〉 2n/(n + 2) our construction gives existence of at least one very weak solution. Furthermore, for r ≥ 3n/(n + 2) we prove that all weak solutions lying in the ball in W01,r of radius smaller than critical are equal. Finally, we obtain an existence result for the flow through a thin slab.
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    On some second-order non-linear systems of a hyperbolic-parabolic type (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 949-957 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We consider local solutions to the Cauchy problem for a class of non-linear hyperbolic-parabolic systems generalizing the systems of elasticity and thermoelasticity. Our main purpose is to relax the usual regularity requirements to include the nonclassical solutions into considerations.
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    Masthead (1995)
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    Mathematical Methods in the Applied Sciences 18 (1995) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    The free streaming operator: A mathematical model for diffusive multiplying boundary conditions (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1165-1180 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: We show that the free streaming operator with diffusive multiplying boundary conditions is the generator of a quasi-bounded semigroup. We also examine some spectral properties of such an operator.
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    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part III: Theory in the case of vertical angular frequency and in the general spin-case (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 201-223 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: If a ball is viewed as a rigid body, its flight in the atmosphere can be described by six ordinary differential equations, which has been derived in the first part of this paper.In this following third part, some further theoretical aspects in the case of vertical angular frequency will be pointed out using an unknown transformation of the original independent variable, i.e. the time, as indicated in Part II.Last, but not least, the general case of angular frequency is to be treated. A rough qualitative discussion of the solutions is given as well as - if the equations are viewed as a three-dimensional dynamical system - the unique stable equilibrium, which depends on the spin. This equilibrium turns out to be globally attractive, which can be proved by the construction of a suitable Ljapunov function. Then, the ball flight system can be transformed into a fourth-order scalar differential equation.
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    Linear symmetric hyperbolic systems with characteristic boundary (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 855-870 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The author studies the mixed problem for the linear symmetric hyperbolic systems with maximally non-negative and characteristic boundary condition. Existence of a unique solution is proved inside a suitable class of functions of weighted Sobolev type which takes account of the loss of regularity in the normal direction to the characteristic boundary.
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    Non-classical interface problems for piecewise homogeneous anisotropic elastic bodies (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 27-49 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: Two non-classical model interface problems for piecewise homogeneous anisotropic bodies are studied. In both problems on the contact surface jumps of the normal components of displacement and stress vectors are given. In addition, in the first problem (Problem H) the tangent components of the displacement vectors are given from both sides of the contact surface, while in the second one (Problem G) the tangent components of the stress vectors are prescribed on the same surface. The existence and uniqueness theorems are proved by means of the boundary integral equation method, and representations of solutions by single layer potentials are established. In the investigation the general approach of regularization of the first kind of integral equations is worked out for the case of two-dimensional closed smooth manifolds. An equivalent global regularizer operator is constructed explicitly in the form of a singular integro-differential operator.
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    Connectivity graphs on two-dimensional surfaces and their application in robotics (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 67-82 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The problem of robot motion planning in an environment with obstacles can often be reduced to the study of connectivity of the robot's free configuration space. In turn, space connectivity can be analysed via the corresponding connectivity graph. For two-degree-of-freedom robots, the free configuration space presents a two-dimensional (2D) surface - a compact subspace of a 2D orientable compact manifold. This paper addresses the following abstract problem: given a compact 2D surface bounded by simple closed curves and lying in an orientable 2D manifold (a sphere, a torus, etc.) and given two points in the subspace, suggest a systematic way of defining the connectivity graph in the subspace, based on its topological properties. The use of space topology results in powerful, from the robotics standpoint, provable algorithms capable of on-line motion planning in an environment with unknown obstacles of arbitrary shapes. This makes the method distinct from other techniques, which require complete information, algebraic representation of space geometry, and off-line computation.
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    On a kinetic model for shallow water waves (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 709-722 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: The system of shallow water waves is one of the classical examples for non-linear, two-dimensional conservation laws. The paper investigates a simple kinetic equation depending on a parameter ∊ which leads for ∊ → 0 to the system of shallow water waves. The corresponding ‘equilibrium’ distribution function has a compact support which depends on the eigenvalues of the hyperbolic system. It is shown that this kind of kinetic approach is restricted to a special class of non-linear conservation laws. The kinetic model is used to develop a simple particle method for the numerical solution of shallow water waves. The particle method can be implemented in a straightforward way and produces in test examples sufficiently accurate results.
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    The problem of primary frost heave with frost penetration (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 995-1011 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper is concerned with a mathematical model for the phenomenon of primary frost heave with frost penetration, which appears in the freezing process of wet soil. The problem is formulated in the form of a free boundary problem with two free boundaries. It is shown that there exists a unique classical solution for this problem.
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    Weak solutions to a non-linear hyperbolic system arising in the theory of dielectric liquids (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1041-1052 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a model of the motion of a viscous dielectric liquid subjected to a DC electric field in the case when the bulk conduction results from the presence of a dissociation-recombination process. The effects of both magnetic field and ionic diffusion are neglected. The existence of at least one weak solution is proved via the method of renormalized solutions.
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    Masthead (1995)
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    Mathematical Methods in the Applied Sciences 18 (1995) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    Periodic solutions for differential equations of order three, with application to heat-flux induced convection (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1133-1164 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In this paper we show the existence of periodic solutions for a class of non-linear regular vector fields of ∝3 admitting the trivial solution and depending on a real parameter μ. Two main assumptions lead to this conclusion: first, the right hand-side of each vector field anticommutes with a reflection. Then, its linear part admits the eigenvalue zero for all variations of μ, and takes the form of a three-dimensional Jordan block at μ = 0. This result allows the description of the bidimensional stationary patterns induced by a uniform heat-flux imposed on the boundaries of an infinite porous layer, saturated by a fluid. Indeed, when the filtration Rayleigh number comes close to its critical value, the field of seepage velocity and the field of temperature can be related to a partial differential equation, which admits a three-dimensional centre manifold. The existence of convective patterns follows. Their length depends on the filtration Rayleigh number, and tends towards infinity when this parameter comes close to its critical value (from above).
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    Global solution to the full one-dimensional Frémond model for shape memory alloys (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 371-385 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, we prove the existence and uniqueness of the solution to the one-dimensional initial-boundary value problem resulting from the Frémond thermomechanical model of structural phase transitions in shape memory materials. In this model, the free energy is assumed to depend on temperature, macroscopic deformation and phase fractions. The resulting equilibrium equations are the balance laws of (linear) momentum and energy, coupled with an evolution variational inequality for the phase fractions. Fourth-order regularizing terms in the quasi-stationary momentum balance equation are not necessary, and, as far as we know for the first time, all the non-linear terms of the energy balance equation are taken into account.
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    Integral equations for the diffraction problems in the wedge (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 449-471 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the present paper we investigated the boundary value problems appearing in the study of diffraction of acoustical or electromagnetic waves on arbitrary bounded body contained within the wedge. The potential theory has been developed making it possible to reduce the boundary value problems to Fredholm integral equations on the body's boundary. We prove existence and uniqueness of solutions for these integral equations and the boundary value problems.For some other types of domains with infinite boundaries similar problems have been studied in [4, 6-8, 12-14, 19, 20, 22, 23, 25-28].
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    General mathematical concept of compensation in sports science with quantitative analysis in the case of sprinting performance (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 473-505 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In many of the known sports disciplines, especially in athletics, the criterion which determines the positions of the competitors is a simple physical value, mostly a time or a distance, and the athlete with the minimum or maximum, respectively, takes the first place. Moreover, sports science explains this criterion by a set of the so-called basic abilities. Compensation means the balance of the inferiority of such a basic ability by the superiority of another one.In the following paper, a general abstract concept to analyse compensation in a quantitative way is presented first. It can be applied to any discipline with a measurable criterion, if, in addition, the performance can be described by a kinematic function.Second, the proceeding is worked out in detail for the short sprint based on the modelling of the velocity function of a sprinter and the indicators for his basic abilities in [6]. The two aspects of compensation, namely the set of indicators which belong to the same criterion and the improvement of the criterion caused by the improvement of a basic ability, are discussed in a quantitative way. They turn out to be describable by the mathematical structures of ‘surfaces of constant pure running time’ and certain gradients, respectively.
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    An application of the limiting absorption principle to a mixed boundary value problem in an infinite strip (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 529-548 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: We present a complete proof of the existence and uniqueness of solutions of a mixed boundary value problem for the homogeneous Laplace equation in an unbounded parallel strip based on the principle of limiting absorption.
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    Study of a perforated thin plate according to the relative sizes of its different parameters (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 571-589 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We are interested in the study of a thin plate, periodicially perforated by cylindrical holes, the axes of which are perpendicular to the plane of the plate. A horizontal section of the plate specifies its geometry, and shows a periodicity in the order of ∊. The thickness of the plate is equal to e. The ratio of material is small, and is characterized by the parameter δ, the thickness of the bars being equal to ∊δ. In this paper, we study the dependence of displacements on e, ∊ and δ, and to give equivalent limits when e, then ∊, and finally δ, tend towards zero. An interesting result obtained in this work is the negative Poisson coefficient of the final equivalent material. Although this coefficient is theoretically between -½ and 1, most materials encountered in practice have a positive one.
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    Uniqueness theorems for a nonlinear Tricomi problem and the related evolution problem (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 591-601 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider an initial-boundary value problem for the non-linear evolution equation in a cylinder Qt = Ω × (0, t), where T[u] = yuxx + uyy is the Tricomi operator and l(u) a special differential operator of first order. In [10] we proved the existence of a generalized solution of problem (1) and the existence of a generalized solution of the corresponding stationary boundary value problem (non-linear Tricomi problem) In this paper we give sufficient conditions for the uniqueness of these solutions.
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    The identification problem for the exponential Radon transform (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 687-695 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The exponential Radon transform, which arises in single photon emission computed tomography, is defined by R ƒ(μ:ω,s) = ∫Rƒ(sω + tomega;⊥) eμt dtƒ. Here ƒ is a compactly supported distribution in the plane which represents the location and intensity of a radio-pharmaceutical in a body of constant, but unknown, attenuation μ, and ω is a direction. The identification problem is to determine the attenuation μ from the data Rƒ with ƒ unknown. We will show that μ can be determined from the data if and only if ƒ is not a radial distribution and give formulae for computing μ when ƒ is not radial.
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    A low velocity approximation for the relativistic Vlasov-Maxwell system (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 739-753 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: An approximation for the relativistic Vlasov-Maxwell (RVM) system of partial differential equations in the one-space, two-momenta case is proposed. The speed of light, c, appears as a parameter in this system. The approximation is obtained by modifying certain integral operators appearing in integral representations, due to Glassey and Strauss, of the electric and magnetic fields, and replaces the hyperbolic Maxwell system with one that is elliptic in nature (for each fixed t). Solutions of the modified problem are shown to converge in a pointwise sense to solutions of (RVM) at the asymptotic rate of 1/c2 as c tends to infinity.
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    The norm and the essential norm of the double layer elastic and hydrodynamic potentials in the space of continuous functions (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1095-1131 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: We study a class of matrix integral operators which appear as limit values of the double layer potentials. We find general representations for the norms and for the essential norms of such operators in the space of continuous vector-valued functions.These representations are specified for boundary integral operators of linear isotropic elasticity theory and hydrodynamics of viscous incompressible fluid under the assumption that there is an angle point on the boundary of a plane domain and a conic point or an edge on the boundary of a three-dimensional domain.
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    On Sommerfeld's half-plane problem for the equations of linear thermoelasticity (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1215-1237 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The Sommerfeld screen problem - well known by many publications studying the several mathematical and physical aspects - is generalized to the linear thermoelastic equations. We derive representation formulas of the solution from the data in the whole plane containing the screen. The corresponding boundary integral equations of Wiener-Hopf type are presented and we obtain important information concerning the factorization of the Wiener-Hopf operators.
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    Initial-boundary value problems in linear viscoelasticity on the half-space (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1181-1214 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: After deriving the linear hereditary constitutive laws for viscoelasticity, deducing frequency representation and the correspondence principle to linear elastodynamics the weak form of the equations of motion and their decomposition into pseudo-wave equations are stated. Applying a Laplace transform in the time domain the Green's tensor is constructed by means of a spatial distributional Fourier transform. A detailed discussion of the four main initial-boundary value problems with prescribed displacement and traction components on the plane {x3 = 0} leads to half-space representations by inverse Fourier integrals. Finally some asymptotic behaviour of the solution in the original time domain is deduced.
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    On an initial boundary value problem for the equations of ideal magneto-hydrodynamics (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 841-853 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study an initial boundary value problem for the symmetric hyperbolic quasilinear system of the equations of ideal magneto-hydrodynamics with a perfectly conducting wall boundary condition. Existence of a unique classical solution is proved inside a suitable class of functions of Sobolev type. Moreover, solutions inside the above class are shown to depend continuously in strong norm on the data.
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    Quaternion non-linear filter for estimation of rotating body attitude (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1239-1255 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A problem of optimal estimation of a rotating vehicle's attitude with both differential equations of motion and observations of stars by onboard equipment is considered. The problem is formulated like a determinate non-linear Kalman filter problem in quaternion terms. An exact analytical solution of the problem is also found in quaternion terms. Various types of solutions in accordance with a mutual arrangement of observed stars are presented. An example of only one observed star is demonstrated to support the method. The method is also suited for geodetic applications, e.g. geodetic positioning and navigation systems.
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    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    Reciprocity relations and completeness of far-field pattern vectors for obstacle scattering of acoustic wave in a stratified medium (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 51-66 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Under a generalized Sommerfeld radiation condition, we proved the uniqueness and existence of the direct obstacle scattering problem of time-harmonic acoustic waves in a stratified medium [8]. In this paper, we study the asymptotic behaviour of the scattered waves and prove three reciprocity relations among the free-wave far-field patterns and the guided-wave far-field pattern vectors corresponding to incident distorted plane waves and normal mode waves. Then we prove conditions under which a set of far-field patterns is complete in a Hilbert space based on the reciprocity relation. These properties are important in investigating the inverse obstacle scattering problems.
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    Continuous dependence of the scattering amplitude on the surface of an obstacle (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 121-126 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: Let Dj,j = 1,2, be two bounded domains (obstacles) in ∝n, n ≥ 2, with the boundaries Γj. Let Aj be the scattering amplitude corresponding to Dj. The Dirichlet boundary condition is assumed on Γj. A formula is derived for A:= A1 - A2. This formula is used for a derivation of the estimate of ∣A1 - A2∣ in terms of the distance d(Γ1, Γ2) between Γ1 and Γ2. If d(Gamma;1, Gamma;2) ≤ ∊, then ∣A∣ ≤ c∊, where c is a positive constant which depends on Γ1 and Γ2 provided that one of the boundaries is of C1,λ class, 0 〈 λ 〈 1, and the other one is a polyhedron which approximates the first one. The results are useful, in particular, for boundary elements method of solving scattering problems.
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    Hyperbolicity of the hydrodynamic model of plasmas under the quasi-neutrality hypothesis (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 627-647 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Collisionless and quasi-neutral hydrodynamic model of plasmas consisting of electrons and several species of ions are investigated. When two species of ions are considered, the hyperbolicity of the system of transport equations obtained in the quasi-neutrality limit leads to a restriction on the magnitude of the admissible relative velocities.
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    Optimal preconditioner for boundary element formulation of the Dirichlet problem in elasticity (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 603-613 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: An optimal preconditioning procedure for the numerical solution of two-dimensional Dirichlet problem for Lamé equations by boundary element method is constructed. An efficient algorithm for the above problem is also developed.
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    Regularising discretizations of the Birkhoff-Rott equation (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 615-625 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A thin shear layer moving from the trailing edge of a two-dimensional aerofoil section downstream can be interpreted as a curve of discontinuity for the tangential velocity and may be approximated by a vortex sheet in inviscid, incompressible fluid flow. It is well known that vortex sheets are subject to instabilities of Kelvin-Helmholtz type which lead to roll-up phenomena in the wake. The motion of such sheets is governed by the Birkhoff-Rott equation. In the case of Kelvin-Helmholtz instability it seems clear that a curvature singularity occurs at a certain critical time and that consistent discretizations of the Birkhoff-Rott equation may fail to yield reliable results even before the time of occurrence of a singularity. We discuss the modification of the Biot-Savart kernel in the sense of Krasny who regularized the kernel by means of a global parameter. Using discrete Fourier transform we show the damping influence of this regularization technique. We modify the kernel carefully by introducing a regularization found in ordinary vortex methods and show that reliable results may be obtained up to and slightly after the singularity formation without increasing the accuracy of the computation.
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    Global in time existence of small solutions of non-linear thermoviscoelastic equations (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 871-895 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove a global in time existence theorem of classical solutions of the initial boundary value problem for a non-linear thermoviscoelastic equation in a bounded domain for very smooth initial data, external forces and heat supply which are very close to a specific constant equilibrium state. Our proof is a combination of a local in time existence theorem and some a priori estimates of local in time solutions. Such a priori estimates are proved basically for suitable linear problems by using some multiplicative techniques. An exponential stability of the constant equilibrium state also follows from our proof of the existence and regularity theorems.
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    Masthead (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995) 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
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    Topics: Mathematics
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    Announcement from the publisher… (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. i 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
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    Optimal-order convergence rates for Eulerian-Lagrangian localized adjoint methods for reactive transport and contamination in groundwater (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 1-31 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Eulerian-Langrangian localized adjoint methods (ELLAM) were developed to solve convection-diffusion-reaction equations governing contaminant transport in groundwater flowing through a porous medium, subject to various combinations of boundary conditions. In this article, we prove optimal-order error estimates and some superconvergence results for the ELLAM schemes. In contrast to many existing estimates for a variety of numerical methods, which often contain the temporal derivatives of the exact solution, our error estimates contain the total derivatives of the exact solution but do not involve any temporal derivatives of the exact solution. © 1995 John Wiley & Sons, Inc.
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    A fourth-order finite difference scheme for two-dimensional nonlinear elliptic partial differential equations (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 33-40 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A finite difference scheme for the two-dimensional, second-order, nonlinear elliptic equation is developed. The difference scheme is derived using the local solution of the differential equation. A 13-point stencil on a uniform mesh of size h is used to derive the finite difference scheme, which has a truncation error of order h4. Well-known iterative methods can be employed to solve the resulting system of equations. Numerical results are presented to demonstrate the fourth-order convergence of the scheme. © 1995 John Wiley & Sons, Inc.
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    Efficient computation of a mathematical model for the damping of pressure waves in tubes of circular form (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 41-60 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A computational method for a system of partial integrodifferential equations of Volterra type is developed. These equations describe the damping of pressure waves in tubes of circular form, taking into account the nonstationary increase of friction. The analytical solution of the model equations is given. A rapidly convergent expansion as well as sharp error estimates for the approximate solutions are obtained. Finally an efficient algorithm using recursion formulas is presented and the algorithm is compared numerically with the method of characteristics. © 1995 John Wiley & Sons, Inc.
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    URL: http://dx.doi.org/10.1002/num.1690110105
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    A primal hybrid finite element method for a strongly nonlinear second-order elliptic problem (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 61-75 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Neumann problem for a strongly nonlinear second-order elliptic equation in divergence form is approximated by primal hybrid finite element methods defined by Raviart and Thomas. Existence and uniqueness of the approximation are proved, and optimal order error estimates are established in various norms. © 1995 John Wiley & Sons, Inc.
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    URL: http://dx.doi.org/10.1002/num.1690110106
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    Finite element approximation of optimal control problems for the von Kármán equations (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 111-125 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This article is concerned with optimal control problems for the von Kármán equations with distributed controls. We first show that optimal solution exist. We then show that Lagrange multipliers may be used to enforce the consstraints and derive an optimality system from which optimal states and controls may be deduced. Finally, we define finite element approximations of solutions for the optimality system and derive error estimate for the approximations. © 1995 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690110109
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    The stability of finite element methods (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 93-109 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We give an abstract stability result for finite element methods. It provides a general guideline for establishing the stability of finite element methods for a given norm once it is established with respect to another norm. The abstract result yields stability estimates of natural norms for finite element methods, which have recently been developed to stabilize effects like dominant convection, incompressibility constraints, or boundary conditions. These stability results simplify the error analysis of the discretizations and are helpful fin the convergence analysis of multigrid methods for the solution of the corresponding discrete problems. © 1995 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690110108
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    Interpolation for solutions of the Helmholtz equation (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 77-91 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the interpolation problem for solutions of the two-dimensional Helmholtz equation, which are sampled along a line. The data are the function values and the normal derivatives at a discrete set of point sensors. A wave transform is used, analogous to the common Fourier transform. The inverse wave transform defines the Hilbert space for oscillatory Helmholtz solutions. We thereby introduce an interpolant that has some advantages over the usual sinc x in the Whittaker-Shannon sampling in one dimension; in particular, coefficients of the two-dimensional solution are invariant under translations and rotations of the sampling line. The analysis is relevant for the optical sampling problem by sensors on a screen. © 1995 John Wiley & Sons, Inc.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690110107
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    Masthead (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995) 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690110201
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    Announcement from the publisher… (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. i 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690110202
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    Difference approximations for wave equations via finite elements II. Error analysis (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 147-163 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Difference-like schemes for the wave equation arise naturally from a Galerkin finite-element formulation, if we adopt certain quadrature rules in evaluating the mass and stiffness matrices. One can extend these schemes to problems involving sharp interfaces by applying the quadrature on a refinement of the finite-element grid that includes the interfaces. We develop error estimates for this modified scheme that corroborate numerical results for acoustic and elastic wave equations, presented in a companion article. © 1995 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690110204
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    Difference approximations for wave equations via finite elements. I. Construction and performance (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 127-146 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Many practical applications of wave equations involve media in which there are interfaces, or discontinuities in material properties. The accurate numerical representation of these interfaces is important in mathematical models. One can develop generalizations of standard finite-difference methods that accommodate sharp interfaces by modifying a straightforward finite-element approach. In two space dimensions, these methods yield explicit, 5-point or 9-point difference schemes that accurately capture reflection, transmission, and refraction at interfaces. The approach also extends readily to the simulation of waves in elastic media. A companion article presents an error analysis for the approach. © 1995 John Wiley & Sons, Inc.
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    An error estimate for a finite volume scheme for a diffusion-convection problem on a triangular mesh (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 165-173 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study here a finite volume scheme for a diffusion-convection equation on an open bounded set Ω of ∝2, using a triangular mesh for the discretization of Ω. The 4-point numerical scheme is presented along with the geometrical assumptions on the mesh. An error estimate of order h on the discrete L2 norm is obtained, where h denotes the “size” of the mesh. The proof uses an estimate of order h of the consistency error on the fluxes and an estimate of the number of edges of the mesh between one given triangle and the boundary Ω. © 1995 John Wiley & Sons, Inc.
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    Least-squares finite element approximation of Fisher's reaction-diffusion equation (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 175-186 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Fisher's equation is a classical diffusion-reaction type of problem describing diffusion and nonlinear reproduction of a species. In the present study we develop a least-squares finite element formulation of Fisher's equation and carry out supporting numerical studies. Of particular interest are questions associated with the approximation of progressive wave solutions with minimum speed and the viability of the least-squares approach for this class of problem. © 1995 John Wiley & Sons, Inc.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690110206
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    Masthead (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995) 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690110301
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    Announcement from the publisher… (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. i 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690110302
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    Technical note: The numerical solution of the system of 3-D nonlinear elliptic equations with mixed derivatives and variable coefficients using fourth-order difference methods (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 187-197 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this article, we report two fourth-order difference methods for the numerical integration of the system of general 3-D nonlinear elliptic equations subject to Dirichlet boundary conditions on a uniform cubic grid. When the coefficients of uxy, uyz, and uzx are not equal to zero and the coefficients of uxx, uyy, and uzz are equal, we require 27 grid points; when the coefficients of uxy, uyz, and uzx are equal to zero, we require only 19 grid points. The utility of the new methods is shown by testing the methods on various examples, including 3-D steady state viscous incompressible Navier-Stokes' model equations and Poisson's equation in polar coordinates, which confirm the accurate and oscillation-free solutions for large Reynolds numbers even in the vicinity of singularity. © 1995 John Wiley & Sons, Inc.
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    URL: http://dx.doi.org/10.1002/num.1690110303
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    Incremental unknowns for solving nonlinear eigenvalue problems: New multiresolution methods (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 199-228 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this article, we present several numerical multilevel schemes for the solution of nonlinear eigenvalue problems. Using the Incremental Unknowns, we construct some generalization of the Marder and Weitzner method, which is well suited for the calculation of unstable solutions. The new methods that we present are based on a different treatment of the several structures appearing with the utilization of the hierarchical preconditioner. We illustrate the efficiency of the new methods with the calculation of unstable solutions of a reaction diffusion problem. © 1995 John Wiley & Sons, Inc.
    Additional Material: 20 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690110304
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    A modified method of characteristics incorporating streamline diffusion (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 255-274 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A hybrid finite-element method, combining ideas from a modified method of characteristics and the streamline diffusion method, delivers accurate solutions to the advection-diffusion equation. An error analysis for the case of tensorial diffusion shows that the lowest-order version of the scheme, which allows one to use a symmetric linear solvers at each time step, possesses first-order accuracy in time and space. Numerical experiments demonstrate the scheme's ability to model advection-dominated transport of solute plumes without distorting sharp fronts. © 1995 John Wiley & Sons, Inc.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690110306
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    Masthead (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995) 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690110401
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