Unconditional uniqueness and non-uniqueness for Hardy-Hénon parabolic equations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866916161691582464 |
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| author | Chikami, Noboru Ikeda, Masahiro Taniguchi, Koichi Tayachi, Slim |
| author_facet | Chikami, Noboru Ikeda, Masahiro Taniguchi, Koichi Tayachi, Slim |
| contents | We study the problems of uniqueness for Hardy-Hénon parabolic equations, which are semilinear heat equations with the singular potential (Hardy type) or the increasing potential (Hénon type) in the nonlinear term. To deal with the Hardy-Hénon type nonlinearities, we employ weighted Lorentz spaces as solution spaces. We prove unconditional uniqueness and non-uniqueness, and we establish uniqueness criterion for Hardy-Hénon parabolic equations in the weighted Lorentz spaces. The results extend the previous works on the Fujita equation and Hardy equations in Lebesgue spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2301_00506 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Unconditional uniqueness and non-uniqueness for Hardy-Hénon parabolic equations Chikami, Noboru Ikeda, Masahiro Taniguchi, Koichi Tayachi, Slim Analysis of PDEs Primary 35A02, 35K58, Secondary 35B33 We study the problems of uniqueness for Hardy-Hénon parabolic equations, which are semilinear heat equations with the singular potential (Hardy type) or the increasing potential (Hénon type) in the nonlinear term. To deal with the Hardy-Hénon type nonlinearities, we employ weighted Lorentz spaces as solution spaces. We prove unconditional uniqueness and non-uniqueness, and we establish uniqueness criterion for Hardy-Hénon parabolic equations in the weighted Lorentz spaces. The results extend the previous works on the Fujita equation and Hardy equations in Lebesgue spaces. |
| title | Unconditional uniqueness and non-uniqueness for Hardy-Hénon parabolic equations |
| topic | Analysis of PDEs Primary 35A02, 35K58, Secondary 35B33 |
| url | https://arxiv.org/abs/2301.00506 |