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Unconditional uniqueness and non-uniqueness for Hardy-Hénon parabolic equations | | Noboru Chikami
; Masahiro Ikeda
; Koichi Taniguchi
; Slim Tayachi
; | | Date: |
2 Jan 2023 | | Abstract: | 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. | | Source: | arXiv, 2301.00506 | | Services: | Forum | Review | PDF | Favorites | |
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