Existence and stability of curved fronts for spatially periodic combustion reaction-diffusion equations in $\mathbb{R}^N$
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912668496953344 |
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| author | Sheng, Wei-Jie Zhang, Xin-Tian |
| author_facet | Sheng, Wei-Jie Zhang, Xin-Tian |
| contents | This paper is concerned with curved fronts of combustion reaction-diffusion equations in spatially periodic media in $\mathbb{R}^N$ $(N\geq2)$. Under the assumption that there are moving pulsating fronts for any given propagation direction $e \in \mathbb{S}^{N-1}$, and by constructing suitable super- and sub-solutions, we prove the existence of a curved front with polytope-like shape in $\mathbb{R}^N$. Then we show that the curved front is unique and asymptotically stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21163 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and stability of curved fronts for spatially periodic combustion reaction-diffusion equations in $\mathbb{R}^N$ Sheng, Wei-Jie Zhang, Xin-Tian Analysis of PDEs 35B10, 35K10, 35K15, 35K57 This paper is concerned with curved fronts of combustion reaction-diffusion equations in spatially periodic media in $\mathbb{R}^N$ $(N\geq2)$. Under the assumption that there are moving pulsating fronts for any given propagation direction $e \in \mathbb{S}^{N-1}$, and by constructing suitable super- and sub-solutions, we prove the existence of a curved front with polytope-like shape in $\mathbb{R}^N$. Then we show that the curved front is unique and asymptotically stable. |
| title | Existence and stability of curved fronts for spatially periodic combustion reaction-diffusion equations in $\mathbb{R}^N$ |
| topic | Analysis of PDEs 35B10, 35K10, 35K15, 35K57 |
| url | https://arxiv.org/abs/2510.21163 |