Optimal singularities of initial data of a fractional semilinear heat equation in open sets

Kotaro Hisa

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arXiv · 2312.10969

Optimal singularities of initial data of a fractional semilinear heat equation in open sets

Kotaro Hisa

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Abstract

We consider necessary conditions and sufficient conditions on the solvability of the Cauchy--Dirichlet problem for a fractional semilinear heat equation in open sets (possibly unbounded and disconnected) with a smooth boundary. Our conditions enable us to identify the optimal strength of the admissible singularity of initial data for the local-in-time solvability and they differ in the interior of the set and on the boundary of the set.

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Kotaro Hisa. 2023-12-18. Optimal singularities of initial data of a fractional semilinear heat equation in open sets. https://arxiv.org/abs/2312.10969

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