Curved fronts of bistable reaction-diffusion equations in spatially periodic media: $N\ge 2$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913639189970944 |
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| author | Guo, Hongjun Wang, Haijian |
| author_facet | Guo, Hongjun Wang, Haijian |
| contents | This paper is concerned with curved fronts of bistable reaction-diffusion equations in spatially periodic media for dimensions $N\geq 2$. The curved fronts concerned are transition fronts connecting $0$ and $1$. Under a priori assumption that there exist moving pulsating fronts in every direction, we show the existence of polytope-like curved fronts with $0$-zone being a polytope and $1$-zone being the complementary set. By reversing some conditions, we also show the existence of curved fronts with reversed $0$-zone and $1$-zone. Furthermore, the curved fronts constructed by us are proved to be unique and asymptotic stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03815 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Curved fronts of bistable reaction-diffusion equations in spatially periodic media: $N\ge 2$ Guo, Hongjun Wang, Haijian Analysis of PDEs This paper is concerned with curved fronts of bistable reaction-diffusion equations in spatially periodic media for dimensions $N\geq 2$. The curved fronts concerned are transition fronts connecting $0$ and $1$. Under a priori assumption that there exist moving pulsating fronts in every direction, we show the existence of polytope-like curved fronts with $0$-zone being a polytope and $1$-zone being the complementary set. By reversing some conditions, we also show the existence of curved fronts with reversed $0$-zone and $1$-zone. Furthermore, the curved fronts constructed by us are proved to be unique and asymptotic stable. |
| title | Curved fronts of bistable reaction-diffusion equations in spatially periodic media: $N\ge 2$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.03815 |