Weak solutions for some reaction-diffusion systems with balance law and critical growth with respect to the gradient
N. Alaa, I. Mounir (2001)
Annales mathématiques Blaise Pascal
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N. Alaa, I. Mounir (2001)
Annales mathématiques Blaise Pascal
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Gonzalo Galiano, Mark Adriaan Peletier (1998)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Liljana Stefanovska, Toma Grcev, Sonja Gegovska-Zajkova (2002)
Visual Mathematics
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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....
Salah Badraoui (1999)
Applicationes Mathematicae
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We are concerned with the boundedness and large time behaviour of the solution for a system of reaction-diffusion equations modelling complex consecutive reactions on a bounded domain under homogeneous Neumann boundary conditions. Using the techniques of E. Conway, D. Hoff and J. Smoller [3] we also show that the bounded solution converges to a constant function as t → ∞. Finally, we investigate the rate of this convergence.
Wei-Ming Ni (2004)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We discuss the stability and instability properties of steady state solutions to single equations, shadow systems, as well as systems. Our basic observation is that the more complicated the pattern are, the more unstable they tend to be.
Xavier Cabré, Joana Terra (2009)
Journal of the European Mathematical Society
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