On the Cauchy problem for a semi-linear hyperdissipative heat equation

Franka Baaske; Romaric Kana Nguedia

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arXiv · 2302.02695

On the Cauchy problem for a semi-linear hyperdissipative heat equation

Franka Baaske·Romaric Kana Nguedia

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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.

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Franka Baaske, Romaric Kana Nguedia. 2023-02-06. On the Cauchy problem for a semi-linear hyperdissipative heat equation. https://arxiv.org/abs/2302.02695

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