Muñoz Hernández, EduardoSovrano, ElisaTaddei, Valentina2025-08-292025-08-292025-02-03Muñoz-Hernández, Eduardo, et al. «Coupled reaction-diffusion equations with degenerate diffusivity: wavefront analysis». Nonlinearity, vol. 38, n.o 3, marzo de 2025, p. 035002. DOI.org (Crossref), https://doi.org/10.1088/1361-6544/ada50d.10.1088/1361-6544/ada50dhttps://hdl.handle.net/20.500.14352/123514We 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.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articlehttps://dx.doi.org/10.1088/1361-6544/ada50dhttps://iopscience.iop.org/article/10.1088/1361-6544/ada50dopen access517Degenerate diffusionCoupled reaction-diffusion equationsTraveling wave solutionWave speedSharp profileEcuaciones diferenciales1202.19 Ecuaciones Diferenciales Ordinarias1202.20 Ecuaciones Diferenciales en derivadas Parciales1202 Análisis y Análisis Funcional