Nonnegative solutions of the heat equation in a cylindrical domain and Widder's theorem
Kin Ming Hui, Kai-Seng Chou · arXiv (Cornell University) · 2022
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.