Initial traces and solvability for a semilinear heat equation on a half space of ${\mathbb R}^N$

Kotaro Hisa; Kazuhiro Ishige; Jin Takahashi

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arXiv · 2209.06398

Initial traces and solvability for a semilinear heat equation on a half space of ${\mathbb R}^N$

Kotaro Hisa·Kazuhiro Ishige·Jin Takahashi

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Abstract

We show the existence and the uniqueness of initial traces of nonnegative solutions to a semilinear heat equation on a half space of ${\mathbb R}^N$ under the zero Dirichlet boundary condition. Furthermore, we obtain necessary conditions and sufficient conditions on the initial data for the solvability of the corresponding Cauchy--Dirichlet problem. Our necessary conditions and sufficient conditions are sharp and enable us to find optimal singularities of initial data for the solvability of the Cauchy--Dirichlet problem.

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Kotaro Hisa, Kazuhiro Ishige, Jin Takahashi. 2022-09-14. Initial traces and solvability for a semilinear heat equation on a half space of ${\mathbb R}^N$. https://arxiv.org/abs/2209.06398

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