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

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  • Diffusion equations with degenerate nonlinear source terms arisein many different applications, e.g., in the theory of epidemics,in models of cortical spreading depression, and in models ofevaporation and condensation in porous media. In this paper, weconsider 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 ofuniform rest states and show that traveling wave trajectoriesconnecting two stable rest states can exist generically only fordiscrete wave speeds. Furthermore, we show that families oftraveling waves with a continuum of wave speeds cannot exist.
    Mathematics Subject Classification: Primary: 35K57, 35B35, 74J30; Secondary: 92C20, 92D30.


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