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Displaying similar documents to “Weak solutions for some reaction-diffusion systems with balance law and critical growth with respect to the gradient”

A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems

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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....

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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.

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En este trabajo se estudia de modo analítico y numérico un problema en ecuaciones diferenciales en derivadas parciales que modela la dinámica de dos poblaciones afectadas por la presión poblacional inter e intraespecíficas y por un potencial medioambiental. Debido a los términos de difusión cruzada, el problema es fuertemente no lineal por lo que el principio del máximo y los métodos relacionados con el mismo no pueden ser aplicados. En primer lugar demostramos la existencia de soluciones...