Comparison theorems for multicomponent diffusion systems: Developments since 1961.
Nelson, M.I. (2000)
Journal of Applied Mathematics and Decision Sciences
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Nelson, M.I. (2000)
Journal of Applied Mathematics and Decision Sciences
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Gonzalo Galiano, Mark Adriaan Peletier (1998)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Nicolas Bouillard, Robert Eymard, Raphaele Herbin, Philippe Montarnal (2007)
ESAIM: Mathematical Modelling and Numerical Analysis
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Modeling the kinetics of a precipitation dissolution reaction occurring in a porous medium where diffusion also takes place leads to a system of two parabolic equations and one ordinary differential equation coupled with a stiff reaction term. This system is discretized by a finite volume scheme which is suitable for the approximation of the discontinuous reaction term of unknown sign. Discrete solutions are shown to exist and converge towards a weak solution of the continuous...
Hideki Murakawa (2009)
Kybernetika
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This paper deals with nonlinear diffusion problems involving degenerate parabolic problems, such as the Stefan problem and the porous medium equation, and cross-diffusion systems in population ecology. The degeneracy of the diffusion and the effect of cross-diffusion, that is, nonlinearities of the diffusion, complicate its analysis. In order to avoid the nonlinearities, we propose a reaction-diffusion system with solutions that approximate those of the nonlinear diffusion problems....