On representation of solutions to the heat equation
Analysis of PDEs
2023-10-31 v1 Classical Analysis and ODEs
Abstract
We propose a simple method to obtain semigroup representation of solutions to the heat equation using a local condition with prescribed growth and a boundedness condition within tempered distributions. This applies to many functional settings and, as an example, we consider the Koch and Tataru space related to initial data.
Keywords
Cite
@article{arxiv.2310.19330,
title = {On representation of solutions to the heat equation},
author = {Pascal Auscher and Hedong Hou},
journal= {arXiv preprint arXiv:2310.19330},
year = {2023}
}