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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2406.14218 |
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| _version_ | 1866911927512334336 |
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| author | Harada, Junichi |
| author_facet | Harada, Junichi |
| contents | The asymptotic bahavior of blowup solutions to the Fujita type heat equation $u_t=Δu+|u|^{p-1}u$ is studied. This equation admits the ODE type blowup given by $u(x,t)=(p-1)^\frac{1}{p-1}(T-t)^{-\frac{1}{p-1}}$. It is known that nondegenerate ODE type blowup is stable if $p\in(1,\frac{n+2}{n-2})$ due to Fermanian Kammerer-Merle-Zaag (2000). This paper extends their result to more general case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14218 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of nondegenerate ODE type blowup for the Fujita type heat equation Harada, Junichi Analysis of PDEs 35B44, 35B35, 35B40 The asymptotic bahavior of blowup solutions to the Fujita type heat equation $u_t=Δu+|u|^{p-1}u$ is studied. This equation admits the ODE type blowup given by $u(x,t)=(p-1)^\frac{1}{p-1}(T-t)^{-\frac{1}{p-1}}$. It is known that nondegenerate ODE type blowup is stable if $p\in(1,\frac{n+2}{n-2})$ due to Fermanian Kammerer-Merle-Zaag (2000). This paper extends their result to more general case. |
| title | Stability of nondegenerate ODE type blowup for the Fujita type heat equation |
| topic | Analysis of PDEs 35B44, 35B35, 35B40 |
| url | https://arxiv.org/abs/2406.14218 |