Traveling waves for bistable reaction-diffusion-convection equations with discontinuous density-dependent coefficients
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918298939031552 |
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| author | Drábek, Pavel Jung, Soyeun Ko, Eunkyung Zahradníková, Michaela |
| author_facet | Drábek, Pavel Jung, Soyeun Ko, Eunkyung Zahradníková, Michaela |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15107 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Traveling waves for bistable reaction-diffusion-convection equations with discontinuous density-dependent coefficients Drábek, Pavel Jung, Soyeun Ko, Eunkyung Zahradníková, Michaela Analysis of PDEs 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. |
| title | Traveling waves for bistable reaction-diffusion-convection equations with discontinuous density-dependent coefficients |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.15107 |