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arXiv · 2311.05385

Coupled reaction-diffusion equations with degenerate diffusivity: wavefront analysis

Eduardo Muñoz-Hernández·Elisa Sovrano·Valentina Taddei
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Abstract

We investigate traveling wave solutions for a nonlinear system of two coupled reaction-diffusion equations characterized by double degenerate diffusivity: \[n_t= -f(n,b), \quad b_t=[g(n)h(b)b_x]_x+f(n,b).\] These systems mainly appear in modeling spatial-temporal patterns during bacterial growth. Central to our study is the diffusion term $g(n)h(b)$, which degenerates at $n=0$ and $b=0$; and the reaction term $f(n,b)$, which is positive, except for $n=0$ or $b=0$. Specifically, the existence of traveling wave solutions composed by a couple of strictly monotone functions for every wave speed in a closed half-line is proved, and some threshold speed estimates are given. Moreover, the regularity of the traveling wave solutions is discussed in connection with the wave speed.

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Eduardo Muñoz-Hernández, Elisa Sovrano, Valentina Taddei. 2023-11-09. Coupled reaction-diffusion equations with degenerate diffusivity: wavefront analysis. https://arxiv.org/abs/2311.05385

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