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2024 Existence and Uniqueness for the Cauchy Problem of Semilinear Heat Equations on Stratified Lie Groups in the Critical Sobolev Space
Hiroyuki Hirayama, Yasuyuki Oka
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Taiwanese J. Math. Advance Publication 1-21 (2024). DOI: 10.11650/tjm/240604

Abstract

The aim of this paper is to give existence and uniqueness results for solutions to the Cauchy problem of semilinear heat equations on stratified Lie groups $\mathbb{G}$ with the small initial data belonging to the critical Sobolev space. We consider a power type nonlinearity that behaves like $|u|^{\alpha}$ or $|u|^{\alpha-1}u$ ($\alpha > 1$).

Funding Statement

This work was supported by JSPS KAKENHI Grant Number JP 21K03333.

Citation

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Hiroyuki Hirayama. Yasuyuki Oka. "Existence and Uniqueness for the Cauchy Problem of Semilinear Heat Equations on Stratified Lie Groups in the Critical Sobolev Space." Taiwanese J. Math. Advance Publication 1 - 21, 2024. https://doi.org/10.11650/tjm/240604

Information

Published: 2024
First available in Project Euclid: 23 June 2024

Digital Object Identifier: 10.11650/tjm/240604

Subjects:
Primary: 35K55 , 35R03

Keywords: Cauchy problem , Semilinear heat equations , stratified Lie groups , well-posedness

Rights: Copyright © 2024 The Mathematical Society of the Republic of China

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