English

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}
}
R2 v1 2026-06-28T08:32:51.145Z