Nonnegative solutions of the heat equation in a cylindrical domain and Widder's theorem
Kin Ming Hui, Kai-Seng Chou
TL;DR
This paper establishes a comprehensive integral representation for all nonnegative solutions of the heat equation in a cylindrical domain, linking solutions to boundary traces and proving their uniqueness.
Contribution
It introduces a novel integral representation involving a trace triple that uniquely characterizes nonnegative heat equation solutions in cylindrical domains.
Findings
Every nonnegative solution has an integral representation with a trace triple.
The trace triple uniquely determines the solution.
The representation involves bottom, corner, and lateral boundary traces.
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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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Differential Equations and Boundary Problems · Numerical methods in inverse problems