

Preprint 27/2004
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.