Excluding blowup at zero points of the potential by means of Liouville-type theorems
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866908340917895168 |
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| author | Guo, Jong-Shenq Souplet, Philippe |
| author_facet | Guo, Jong-Shenq Souplet, Philippe |
| contents | We prove a local version of a (global) result of Merle and Zaag about ODE behavior of solutions near blowup points for subcritical nonlinear heat equations. As an application, for the equation $u_t= Δu+V(x)f(u)$, we rule out the possibility of blowup at zero points of the potential $V$ for monotone in time solutions when $f(u)\sim u^p$ for large $u$, both in the Sobolev subcritical case and in the radial case. This solves a problem left open in previous work on the subject. Suitable Liouville-type theorems play a crucial role in the proofs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1605_03558 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Excluding blowup at zero points of the potential by means of Liouville-type theorems Guo, Jong-Shenq Souplet, Philippe Analysis of PDEs We prove a local version of a (global) result of Merle and Zaag about ODE behavior of solutions near blowup points for subcritical nonlinear heat equations. As an application, for the equation $u_t= Δu+V(x)f(u)$, we rule out the possibility of blowup at zero points of the potential $V$ for monotone in time solutions when $f(u)\sim u^p$ for large $u$, both in the Sobolev subcritical case and in the radial case. This solves a problem left open in previous work on the subject. Suitable Liouville-type theorems play a crucial role in the proofs. |
| title | Excluding blowup at zero points of the potential by means of Liouville-type theorems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1605.03558 |