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arXiv · 2601.15107

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

Pavel Drábek·Soyeun Jung·Eunkyung Ko·Michaela Zahradníková
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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.

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Pavel Drábek, Soyeun Jung, Eunkyung Ko, Michaela Zahradníková. 2026-01-21. Traveling waves for bistable reaction-diffusion-convection equations with discontinuous density-dependent coefficients. https://arxiv.org/abs/2601.15107

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