Traveling waves for combustion reaction-diffusion-convection equations: the full range of wave speeds
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arXiv
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| Format: | Preprint |
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2026
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| author | Drábek, Pavel Jung, Soyeun Ko, Eunkyung Zahradníková, Michaela |
| author_facet | Drábek, Pavel Jung, Soyeun Ko, Eunkyung Zahradníková, Michaela |
| contents | We consider traveling wave solutions to a reaction--diffusion--convection equation with a combustion-type reaction term. While a necessary condition for the existence of traveling waves is $c \geq H^*:=\sup_{0<u \leq θ} \big(-\frac{1}{u} \int_0^u h(σ)\,dσ\big)$, where $c$ denotes the wave speed, $θ\in(0,1)$ the ignition threshold, and $h$ the convective term, the available results in \cite{DZ25,MM03} establish existence and nonexistence only under the restriction $c \geq -\min_{u\in[0,1]} h(u)$. In this note, we close this gap by covering the entire range $c\ge H^*$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00638 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Traveling waves for combustion reaction-diffusion-convection equations: the full range of wave speeds Drábek, Pavel Jung, Soyeun Ko, Eunkyung Zahradníková, Michaela Analysis of PDEs We consider traveling wave solutions to a reaction--diffusion--convection equation with a combustion-type reaction term. While a necessary condition for the existence of traveling waves is $c \geq H^*:=\sup_{0<u \leq θ} \big(-\frac{1}{u} \int_0^u h(σ)\,dσ\big)$, where $c$ denotes the wave speed, $θ\in(0,1)$ the ignition threshold, and $h$ the convective term, the available results in \cite{DZ25,MM03} establish existence and nonexistence only under the restriction $c \geq -\min_{u\in[0,1]} h(u)$. In this note, we close this gap by covering the entire range $c\ge H^*$. |
| title | Traveling waves for combustion reaction-diffusion-convection equations: the full range of wave speeds |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2606.00638 |