Existence of front solutions in degenerate reaction diffusion systems

Steffen Heinze, Ben Schweizer, and Hartmut Schwetlick
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Submission date: 05. May. 2004
Pages: 25
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Abstract:
We investigate the dynamics of a system of two reaction diffusion equations in one space dimension, and study the effect of a small and of a vanishing diffusion coefficient in one equation. The analysis is restricted to competing species with two stable equilibria. We show that the system has traveling front solutions and analyze their wave-speed. It turns out that the diffusive species can propagate at a finite rate, while the non-diffusive species is blocked. We characterize the two cases with the help of an Lyapunov function.