Blow-up rate for the subcritical semilinear heat equation in non-convex domains
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909857524744192 |
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| author | Miura, Hideyuki Takahashi, Jin Zhanpeisov, Erbol |
| author_facet | Miura, Hideyuki Takahashi, Jin Zhanpeisov, Erbol |
| contents | We consider the semilinear heat equation $u_t=Δu+|u|^{p-1} u$ in possibly non-convex and unbounded domains. Our main result shows the nonexistence of type II blow-up for possibly sign-changing solutions in the energy subcritical range $(n-2)p<n+2$. This resolves a long-standing open question dating back to the 1980s and also deduces the blow-up of the scaling critical norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17229 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Blow-up rate for the subcritical semilinear heat equation in non-convex domains Miura, Hideyuki Takahashi, Jin Zhanpeisov, Erbol Analysis of PDEs 35K58 We consider the semilinear heat equation $u_t=Δu+|u|^{p-1} u$ in possibly non-convex and unbounded domains. Our main result shows the nonexistence of type II blow-up for possibly sign-changing solutions in the energy subcritical range $(n-2)p<n+2$. This resolves a long-standing open question dating back to the 1980s and also deduces the blow-up of the scaling critical norm. |
| title | Blow-up rate for the subcritical semilinear heat equation in non-convex domains |
| topic | Analysis of PDEs 35K58 |
| url | https://arxiv.org/abs/2510.17229 |