Self-sustaining traveling fronts for a model related to bushfires
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866913812987248640 |
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| author | Dipierro, Serena Valdinoci, Enrico Wheeler, Glen Wheeler, Valentina-Mira |
| author_facet | Dipierro, Serena Valdinoci, Enrico Wheeler, Glen Wheeler, Valentina-Mira |
| contents | This article investigates a mathematical model for bushfire propagation, focusing on the existence and properties of translating solutions. We obtain quantitative bounds on the environmental diffusion coefficient and ignition kernels, identifying conditions under which fires either propagate across the entire region or naturally extinguish.
Our analysis also reveals that vertically translating solutions do not exist, whereas traveling wave solutions with a front moving at any prescribed velocity always exist for kernels that are either of mild intensity or short range. These traveling waves exhibit unbounded profiles.
Although evolutionary unstable, these traveling waves demonstrate stability under perturbations localized in a small region. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21365 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-sustaining traveling fronts for a model related to bushfires Dipierro, Serena Valdinoci, Enrico Wheeler, Glen Wheeler, Valentina-Mira Analysis of PDEs 35C07, 35K10, 45H05, 92-10 This article investigates a mathematical model for bushfire propagation, focusing on the existence and properties of translating solutions. We obtain quantitative bounds on the environmental diffusion coefficient and ignition kernels, identifying conditions under which fires either propagate across the entire region or naturally extinguish. Our analysis also reveals that vertically translating solutions do not exist, whereas traveling wave solutions with a front moving at any prescribed velocity always exist for kernels that are either of mild intensity or short range. These traveling waves exhibit unbounded profiles. Although evolutionary unstable, these traveling waves demonstrate stability under perturbations localized in a small region. |
| title | Self-sustaining traveling fronts for a model related to bushfires |
| topic | Analysis of PDEs 35C07, 35K10, 45H05, 92-10 |
| url | https://arxiv.org/abs/2504.21365 |