Systems of coupled diffusion equations with degenerate nonlinear source terms: Linear stability and traveling waves

Document Type

Article

Publication Date

1-1-2009

Abstract

Diffusion equations with degenerate nonlinear source terms arise in many different applications, e.g., in the theory of epidemics, in models of cortical spreading depression, and in models of evaporation and condensation in porous media. In this paper, we consider a generalization of these models to a system of n coupled diffusion equations with identical nonlinear source terms. We determine simple conditions that ensure the linear stability of uniform rest states and show that traveling wave trajectories connecting two stable rest states can exist generically only for discrete wave speeds. Furthermore, we show that families of traveling waves with a continuum of wave speeds cannot exist.

Identifier

60949107742 (Scopus)

Publication Title

Discrete and Continuous Dynamical Systems

External Full Text Location

https://doi.org/10.3934/dcds.2009.23.561

ISSN

10780947

First Page

561

Last Page

569

Issue

1-2

Volume

23

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