Traveling waves for bistable reaction-diffusion-convection equations with discontinuous density-dependent coefficients

Abstract

Continuing our previous study \cite{DJKZ} on the monostable reaction-diffusion-convection equation, we analyze the bistable case under weak regularity assumptions. Our approach applies monostable results on the subintervals where the reaction term $g$ has constant sign, thereby establishing both existence and nonexistence of bistable traveling wave solutions. We extend the results of \cite{MMM04}, obtained for $p=2$ under higher regularity assumptions ($d\in C^1[0,1]$, $g,h\in C[0,1]$), to the $p$-Laplacian with $p>1$ in our weak regularity setting.