On the Cauchy problem for a semi-linear hyperdissipative heat equation
Analysis of PDEs
2023-02-07 v1
Abstract
The paper is concerned with the Cauchy problem for a semi-linear hyperdissipative heat equation in Besov and Triebel-Lizorkin spaces which is related to the generalized Gauss-Weierstrass semi-group via Duhamel's principle. Using caloric smoothing properties of the semi-group we prove existence and uniqueness of mild and strong solutions which are local in time. Moreover, we study well-posedness of the problem.
Keywords
Cite
@article{arxiv.2302.02695,
title = {On the Cauchy problem for a semi-linear hyperdissipative heat equation},
author = {Franka Baaske and Romaric Kana Nguedia},
journal= {arXiv preprint arXiv:2302.02695},
year = {2023}
}