Unconditional uniqueness and non-uniqueness for Hardy-Hénon parabolic equations

Fuente: arXiv
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Main Authors: Chikami, Noboru, Ikeda, Masahiro, Taniguchi, Koichi, Tayachi, Slim
Format: Preprint
Published: 2023
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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
id 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