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 \(\mathbb{G}\) with the homogeneous dimension \(N\). We consider the nonlinear function behaves like \(|u|^{\alpha}\) or \(|u|^{\alpha-1}u\) \(...

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Bibliographic Details
Published in:arXiv.org 2024-04
Main Authors: Hirayama, Hiroyuki, Oka, Yasuyuki
Format: Article
Language:English
Subjects:
Cauchy problems
Euclidean geometry
Euclidean space
Fourier analysis
Lie groups
Mathematical analysis
Sobolev space
Thermodynamics
Uniqueness
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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 \(\mathbb{G}\) with the homogeneous dimension \(N\). We consider the nonlinear function behaves like \(|u|^{\alpha}\) or \(|u|^{\alpha-1}u\) \((\alpha>1)\) and the initial data \(u_0\) belongs to the Sobolev spaces \(L^p_s(\mathbb{G})\) for \(1
ISSN:2331-8422
DOI:10.48550/arxiv.2404.03128