Year: 2023
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Baaske, Franka, Nguedia, Romaric Kana
Institutions: Hochschule Mittweida, Friedrich Schiller University Jena
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4319453255