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arXiv · 2412.06200

Initial traces of solutions to a semilinear heat equation under the Dirichlet boundary condition

Kotaro Hisa·Kazuhiro Ishige
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Abstract

We study qualitative properties of initial traces of nonnegative solutions to a semilinear heat equation in a smooth domain under the Dirichlet boundary condition. Furthermore, for the corresponding Cauchy--Dirichlet problem, we obtain sharp necessary conditions and sufficient conditions on the existence of nonnegative solutions and identify optimal singularities of solvable nonnegative initial data.

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Kotaro Hisa, Kazuhiro Ishige. 2024-12-09. Initial traces of solutions to a semilinear heat equation under the Dirichlet boundary condition. https://arxiv.org/abs/2412.06200

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