Local solvability and dilation-critical singularities of supercritical fractional heat equations
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
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| _version_ | 1866909123031859200 |
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| author | Fujishima, Yohei Hisa, Kotaro Ishige, Kazuhiro Laister, Robert |
| author_facet | Fujishima, Yohei Hisa, Kotaro Ishige, Kazuhiro Laister, Robert |
| contents | We consider the Cauchy problem for fractional semilinear heat equations with supercritical nonlinearities and establish both necessary conditions and sufficient conditions for local-in-time solvability. We introduce the notion of a dilation-critical singularity (DCS) of the initial data and show that such singularities always exist for a large class of supercritical nonlinearities. Moreover, we provide exact formulae for such singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05240 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Local solvability and dilation-critical singularities of supercritical fractional heat equations Fujishima, Yohei Hisa, Kotaro Ishige, Kazuhiro Laister, Robert Analysis of PDEs We consider the Cauchy problem for fractional semilinear heat equations with supercritical nonlinearities and establish both necessary conditions and sufficient conditions for local-in-time solvability. We introduce the notion of a dilation-critical singularity (DCS) of the initial data and show that such singularities always exist for a large class of supercritical nonlinearities. Moreover, we provide exact formulae for such singularities. |
| title | Local solvability and dilation-critical singularities of supercritical fractional heat equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2308.05240 |