RT Journal Article
T1 Coupled reaction-diffusion equations with degenerate diffusivity: wavefront analysis
A1 Muñoz Hernández, Eduardo
A1 Sovrano, Elisa
A1 Taddei, Valentina
AB 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.
PB IOP Publishing (IOP Science)
YR 2025
FD 2025-02-03
LK https://hdl.handle.net/20.500.14352/123514
UL https://hdl.handle.net/20.500.14352/123514
LA eng
NO Muñoz-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.
NO Università di Modena e Reggio Emilia, Italy
NO Ministry of Science and Innovation of Spain
DS Docta Complutense
RD 4 sept 2025