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

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. (c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This passage discusses the relationship between nonnegative solutions of the heat equation in a bounded cylindrical domain and their integral representation in terms of a trace triple.