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

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)561-569
Journal / PublicationDiscrete and Continuous Dynamical Systems
Issue number1-2
Publication statusPublished - Jan 2009


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.

Research Area(s)

  • Applications, Diffusion equations with degenerate nonlinear sources, Linear stability, Traveling waves

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