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

TL;DR

This paper investigates the existence of traveling wave solutions in bistable reaction-diffusion-convection equations with discontinuous coefficients, extending previous results to the p-Laplacian case under weaker regularity assumptions.

Contribution

It extends prior monostable wave results to the bistable case for p-Laplacian equations with discontinuous coefficients, under weaker regularity conditions.

Findings

Established existence and nonexistence of bistable traveling waves.

Extended results to p-Laplacian with p>1.

Applied monostable results on subintervals with constant sign of reaction term.

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.