%0 Journal Article
%A Muñoz Hernández, Eduardo
%A Sovrano, Elisa
%A Taddei, Valentina
%T Coupled reaction-diffusion equations with degenerate diffusivity: wavefront analysis
%D 2025
%U https://hdl.handle.net/20.500.14352/123514
%X 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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