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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
27/2004

Existence of front solutions in degenerate reaction diffusion systems

Steffen Heinze, Ben Schweizer and Hartmut Schwetlick

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.

Received:
May 5, 2004
Published:
May 5, 2004

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Preprint
2004 Repository Open Access
Steffen Heinze, Ben Schweizer and Hartmut R. Schwetlick

Existence of front solutions in degenerate reaction diffusion systems