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arXiv · 2210.10954

Nonnegative solutions of the heat equation in a cylindrical domain and Widder's theorem

Kin Ming Hui·Kai-Seng Chou
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Abstract

It is shown every nonnegative solution of the heat equation in a bounded cylindrical domain has an integral representation in terms of a trace triple consisting of a bottom trace, a corner trace and a lateral trace on its parabolic boundary. Conversely this trace triple uniquely determines the solution.

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Kin Ming Hui, Kai-Seng Chou. 2022-10-20. Nonnegative solutions of the heat equation in a cylindrical domain and Widder's theorem. https://arxiv.org/abs/2210.10954

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