Results of existence and uniqueness for the Cauchy problem of semilinear heat equations on stratified Lie groups

The aim of this paper is to give existence and uniqueness results for solutions of the Cauchy problem for semilinear heat equations on stratified Lie groups G with the homogeneous dimension N. We consider the nonlinear function behaves like |u|α or |u|α−1u(α>1) and the initial data u0 belongs to...

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Bibliographic Details
Published in:Journal of Differential Equations 2024-12, Vol.412, p.214-249
Main Authors: Hirayama, Hiroyuki, Oka, Yasuyuki
Format: Article
Language:English
Subjects:
Cauchy problem
Semi linear heat equations
Stratified Lie groups
Well-posedness
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Summary:The aim of this paper is to give existence and uniqueness results for solutions of the Cauchy problem for semilinear heat equations on stratified Lie groups G with the homogeneous dimension N. We consider the nonlinear function behaves like |u|α or |u|α−1u(α>1) and the initial data u0 belongs to the Sobolev spaces Lsp(G) for 1
ISSN:0022-0396
DOI:10.1016/j.jde.2024.08.027