Local solvability and dilation-critical singularities of supercritical fractional heat equations

Yohei Fujishima; Kotaro Hisa; Kazuhiro Ishige; Robert Laister

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arXiv · 2308.05240

Local solvability and dilation-critical singularities of supercritical fractional heat equations

Yohei Fujishima·Kotaro Hisa·Kazuhiro Ishige·Robert Laister

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Abstract

We consider the Cauchy problem for fractional semilinear heat equations with supercritical nonlinearities and establish both necessary conditions and sufficient conditions for local-in-time solvability. We introduce the notion of a dilation-critical singularity (DCS) of the initial data and show that such singularities always exist for a large class of supercritical nonlinearities. Moreover, we provide exact formulae for such singularities.

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Yohei Fujishima, Kotaro Hisa, Kazuhiro Ishige, Robert Laister. 2023-08-09. Local solvability and dilation-critical singularities of supercritical fractional heat equations. https://arxiv.org/abs/2308.05240

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