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  • 1995-1999  (539)
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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.
    Type of Medium: Electronic Resource
    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.
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    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
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    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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    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
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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
    Topics: Mathematics
    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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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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    Analytical solutions of mass transport problems for error estimation of finite/infinite element methods (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 13-23 
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    ISSN: 1069-8299
    Keywords: mass transport problems ; error estimation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In order to make an exact estimation of discretization error for finite/infinite element methods, it is necessary to develop analytical solutions for some transient mass transport problems in infinite media. These transient mass transport problems may be viewed as the benchmark problems for the discretization error estimation of a new numerical method so that they generally have the following characteristics: (1) their initial and boundary conditions can be exactly modelled by the finite/infinite element method; (2) their solutions can be rigorously expressed in a closed form. In this paper, several of the aforementioned problems have been constructed and solved mathematically for transient mass transport problems in both 1D and 2D infinite media.
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    Solution of the differential Riccati equation using the transmission line modelling (TLM) technique (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 25-32 
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    ISSN: 1069-8299
    Keywords: Riccati equation ; transmission line modelling ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this communication, the application of the transmission line modelling (TLM) technique to the solution of the differential Riccati equation is described. A comparison is made between the TLM, fourth-order Runge-Kutta and the first-order Gear methods, for the case where one is applying the Kalman filter to the estimation of a voltage in a passive analogue circuit. In the particular example studied, the state equation is second-order. It is found that, when the system is underdamped, the fourth-order Runge-Kutta method has the best performance, followed by the TLM method. When the system is overdamped and stiff, the TLM method yields results that are closest to the analytical solution. Finally, a discussion is presented of the effects of errors in the TLM solution of the Riccati equation on the accuracy of the solution to the continuous Kalman filter estimation equation.
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    Influence of contact area on service life of gears with crack in tooth root (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 49-58 
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    ISSN: 1069-8299
    Keywords: gears ; fracture mechanics ; service life ; fatigue process ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper describes the influence of contact area on the service life of dynamically loaded gears with a crack in a tooth root. Numerical results obtained with the finite element method using the program package BERSAFE are compared with the experimental results obtained on the universal testing machine INSTRON 1255. Numerical and experimental results are in good agreement. The analysis shows that the contact area directly influences the speed and direction of the crack propagation and the service life of the gear with a crack in a tooth root.
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    Transverse shear correction factors for laminates in cylindrical bending (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 41-47 
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    ISSN: 1069-8299
    Keywords: shear correction ; laminates ; cylindrical bending hypothesis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Mindlin-type plate and shell finite elements are the most widely used ones in the analysis of laminated composite structures. In the commercially available finite element programs, the transverse shear correction factors for these elements are usually the same as for structures made of isotropic materials. In the paper the shear correction factors are determined using energy principles for general laminates in cylindrical bending. Results for various materials and laminates are presented.
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    A B-spline finite element method for the regularized long wave equation (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 59-68 
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    ISSN: 1069-8299
    Keywords: RLW equation ; finite elements ; splines ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A B-spline finite element method is used to solve the regularized long wave equation numerically. This approach involves a Galerkin method with quadratic B-spline finite elements so that there is continuity of the dependent variable and its first derivative throughout the solution range. Time integration of the resulting system of ordinary differential equations is effected using a Crank-Nicolson approximation. Standard problems are used to validate the algorithm, which is then used to model the smooth development of an undular bore.
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    Modified calculation of the dissipation term in thermoplastic finite element equations (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 69-72 
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    ISSN: 1069-8299
    Keywords: finite element method ; thermoplasticity ; internal dissipation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper, a simple modification of the internal dissipation term in coupled thermoplastic finite element equations is presented. A modified form of the heat capacity and the thermomechanical coupling matrices are derived. These modifications are based on a decomposition of the internal dissipation term into two parts, which depend on the total strain rate and the rate of temperature change, respectively.
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    Conference diary (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 91-92 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    Announcements (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 93-94 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    On boundary conditions for unbounded flows (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 179-185 
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    ISSN: 1069-8299
    Keywords: finite elements ; fluid flow ; open boundaries ; Sommerfield boundary conditions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We examine a method to impose boundary conditions on arbitrary boundaries, introduced to make domains of infinite extent finite for the purpose of numerical calculations, when a finite element discretization based on linear, bilinear or trilinear elements is used, in one, two or three dimensions, respectively. In particular, we look at the so-called ‘free’ boundary condition, which consists in retaining the boundary integrals generated by the weighted-residuals formulation along the open boundaries and adding them to the stiffness matrix. We show that this procedure is exactly equivalent to imposing on the boundary nodes a Sommerfeld radiation condition in one dimension, and a slightly modified form of the Sommerfeld boundary condition in two and three dimensions. We also show that the procedure is not applicable to the purely elliptic case.
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    Announcements (1995)
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    Communications in Numerical Methods in Engineering 11 (1995), S. 189-190 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    Conference diary (1995)
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    Communications in Numerical Methods in Engineering 11 (1995), S. 187-188 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    Masthead (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995) 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    Structural improvement of planar triangulations: Some constraints and practical issues (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 191-198 
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    ISSN: 1069-8299
    Keywords: triangulations ; mesh relaxation ; computational geometry ; planar mesh generation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Recent advances in planar mesh generation of arbitrary domains incorporate methods for placing points as well as connecting them into a triangulation. Postprocessing techniques such as Laplacian smoothing and mesh relaxation enhance the shape of triangles in these meshes but do not address the construction of meshes near boundaries or provide a criterion to determine the number of interior points of the initial triangulation. The paper addresses these issues by investigating the construction of degree-6 triangulations, the primary goal of the mesh relaxation method.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640110302
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    Distributed finite element structural analysis using the client-server model (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 227-233 
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    ISSN: 1069-8299
    Keywords: finite element analysis ; distributed computing ; structures ; client-server model ; remote procedure calls ; structural mechanics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a distributed computing approach for concurrent finite element analysis of truss structures. The client-server model of distributed computation is applied to the plane frame finite element algorithm and implemented on SUN workstations. The remote procedure call combined with the ability to create threads of computation allows one to efficiently implement distributed and concurrent programs. The present approach is demonstrated through a typical truss structure to illustrate the details of the implementation. This approach can be used for very large finite element systems.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110305
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    Fluid flows around turbomachinery using an explicit pseudo-temporal Euler FEM (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 199-211 
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    ISSN: 1069-8299
    Keywords: SUPG ; Petrov-Galerkin methods ; finite elements ; explicit scheme ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This work is devoted to the simulation by finite elements of nearly incompressible inviscid flows in real 3D geometries, by means of an Euler code based on the SUPG (streamline upwind Petrov-Galerkin) method, explicit forward Euler pseudo-temporal time integration and periodic and absorbing boundary conditions, among other features. The main goal is the application to flow around turbomachinery, with special emphasis on the performance analysis of a given machine, that involves several numerical computations at different operation points. Finally, these results are summarized in the form of characteristic curves.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110303
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    A posteriori finite element method error estimates for fourth-order problems (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 213-226 
    Details
    ISSN: 1069-8299
    Keywords: a posteriori error estimates ; asymptotic exactness ; finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A posteriori error estimation for typical Euler-Bernoulli beam bending problems is developed using a recovery operator based on a smoothing technique that is applied in the context of one-dimensional fourth-order problems. The development exploits a discrete superconvergence property of the ‘bending moments’ of the trial space interpolant of a polynomial solution of sufficiently low degree at certain Gauss points, and the superconvegence property of the energy norm difference of the trial space interpolant (of the weak solution) and the finite element approximation. An asymptotically exact error estimator is developed.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640110304
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    A superposition method for the solution of crack problems (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 243-254 
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    ISSN: 1069-8299
    Keywords: fracture ; boundary elements ; superposition ; stress intensity factor ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We discuss a two-step superposition method for calculating linear elastic stress intensity factors. The procedure requires the solution to the full cracked problem and the solution to a problem on the same mesh assuming the singularity due to a crack tip in an infinite region. We show that this is equivalent to the well known subtraction of singularity method if the two solutions are characterized by crack tip stress. The advantages of our procedure are that no modifications need to be made to a standard computer program and that once one singular solution is available on a given cracked mesh, solutions with different boundary conditions on the same mesh may be obtained in one step without including any singular crack effects. The mesh required to represent the singular crack tip field may also be studied independently of the complete problem. The additional computational cost of a two-step procedure is minimal since the solution matrix from step one may be reused with a new right-hand side. Numerical experiments using the boundary element method demonstrate the high accuracy and simplicity of the superposition approach.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640110307
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    Selecting upwind parameters for improved iterative performance (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 235-242 
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    ISSN: 1069-8299
    Keywords: upwinding ; iterative methods ; convection-diffusion ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The effect of upwinding on iterative performance of convection-diffusion problems is investigated. An analysis of the iterative method considered here leads to a criterion for selecting the optimal upwinding parameter to improve iterative performance for a class of two-dimensional convection-diffusion problems. Supporting numerical experiments are presented.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640110306
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    A numerical solution for dynamic interaction between rigid wheel and flexible beam (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 267-279 
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    ISSN: 1069-8299
    Keywords: dynamic interaction ; rigid wheel ; flexible beam ; contact force ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method is presented for the analysis of dynamic interaction between rigid wheel and flexible beam. In contrast to traditional approaches, the wheel nominal motion as well as the contact force are considered here as unknowns. The correct contact force between the wheel and the beam is computed by iteratively reducing the constraint error towards zero, and a simple time integration is employed for the solution of equations of motion. Convergence of the iterative scheme is analysed, and numerical simulations are conducted to demonstrate the accuracy of the solution.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640110309
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    The h-, p- and hp-versions of the BEM in elasticity: Numerical results (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 255-265 
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    ISSN: 1069-8299
    Keywords: boundary element method ; error estimation ; hp-version ; Galerkin BEM ; numerical results ; elasticity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper investigates the convergence of the h-, p- and hp-versions of a variational symmetric boundary element method (BEM) in plane elasticity by numerical experiments. The study discusses mixed boundary value problems on polygonal domains, i.e. problems for which the exact solution is analytic except in a finite number of points. The convergence of the error in energy norm is displayed for all versions of the BEM. All results are also compared with those obtained by the corresponding finite element methods. The theoretically predicted asymptotic convergence rates for all versions of the method can be observed in the numerical experiments. A comparison of computer times is given as well.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640110308
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    Background to bench marks, edited by G. E. O. Davies, R. T. Fenner and R. W. Lewis, NAFEMS, Birniehill, East Kilbride, Glasgow. ISBN 1 874376 10 7 (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 281-282 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110310
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    Conference diary (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 283-284 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110311
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    Announcements (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 285-286 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110312
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    Masthead (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110401
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    On the eigenvalues basic to the analytical solution of convective heat transfer with axial diffusion effects (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 287-296 
    Details
    ISSN: 1069-8299
    Keywords: eigenvalues ; integral transforms ; analytical methods ; convection ; Sturm-Liouville system ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The integral transform method is employed in the analytical solution of the non-classical eigenvalue problem that appears in connection with the analysis of forced convection in ducts, including the effect of fluid heat diffusion in the axial direction. The related eigenfunctions are expanded in terms of eigenfunctions from a simpler auxiliary eigenvalue problem, and the original eigenvalues are determined from the associated matrix eigensystem analysis. Convergence rates of the proposed solutions are illustrated and reference results established for different values of the governing parameters.
    Additional Material: 4 Tab.
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    URL: http://dx.doi.org/10.1002/cnm.1640110402
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    Permanent heavy waves in circular-shaped channels (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 355-362 
    Details
    ISSN: 1069-8299
    Keywords: permanent heavy waves ; circular shaped channels ; conformal mapping ; Fatou's method ; Levi-Civita's decomposition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Because of the earth's curvature, all existing channels have a curvature. E. Zeidler gave an existence and uniqueness proof for permanent heavy and capillar-heavy waves in such circular shaped channels. Based on this proof and on a general computational method for constructing the solutions numerically, the case of permanent heavy waves in circular-shaped channels is considered in this work.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640110409
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    Introduction to finite and boundary element methods for engineers, by G. Beer and J. O. Watson, John Wiley and Sons, Chichester, U.K. ISBN 0-471-92813-5. £29.95/$49.95, Program disk £19.95 (extra) (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 373-374 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110411
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    Conference diary (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 375-377 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110412
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