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  • Life and Medical Sciences  (1,847)
  • Cell & Developmental Biology  (1,337)
  • Biochemistry and Biotechnology  (854)
  • Mathematics and Statistics  (129)
  • Wiley-Blackwell  (2,830)
  • 1995-1999  (2,830)
  • 1995  (2,830)
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  • Wiley-Blackwell  (2,830)
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  • 1995-1999  (2,830)
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  • 1
    Electronic Resource
    Electronic Resource
    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
    Electronic Resource
    Electronic Resource
    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 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670180405
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  • 3
    Electronic Resource
    Electronic Resource
    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 
    Details
    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
    Electronic Resource
    Electronic Resource
    Boundary layer resolution in hierarchical plate modelling (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 345-370 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670180503
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  • 5
    Electronic Resource
    Electronic Resource
    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 
    Details
    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
    Electronic Resource
    Electronic Resource
    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 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670181006
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  • 7
    Electronic Resource
    Electronic Resource
    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 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An explicit solution of the pseudo-hyperbolic initial boundary value problem with a mixed boundary condition has been constructed. The problem describes the propagation of non-stationary internal waves in a stratified and rotational fluid. The generation of waves is caused by small oscillations of double-sided plates beginning at time t = 0. Dynamic pressure is specified on one set of plates and this yields the first boundary condition. Normal velocities are specified on another set of plates and this leads to an analogue of the second boundary condition with time derivatives. The solution has been obtained by the method of non-classical time-dependent dynamic potentials. The uniqueness of the solution has been studied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670181105
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  • 8
    Electronic Resource
    Electronic Resource
    A discrete velocity coagulation-fragmentation model (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 959-993 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670181204
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  • 9
    Electronic Resource
    Electronic Resource
    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 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670181304
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  • 10
    Electronic Resource
    Electronic Resource
    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 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670181302
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