English

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 L2L^2 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 BMO1BMO^{-1} 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}
}