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.
Nous proposons une méthode simple pour obtenir une représentation par semi-groupe des solutions de l’équation de la chaleur utilisant une condition à poids et un contrôle dans des distributions tempérées. Cette méthode s’applique à de nombreux espaces fonctionnels. À titre d’exemple, nous considérons l’application aux solutions dans l’espace de Koch et Tataru lié aux données initiales dans .
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Pascal Auscher 1; Hedong Hou 1
CC-BY 4.0
@article{CRMATH_2024__362_G7_761_0,
author = {Pascal Auscher and Hedong Hou},
title = {On representation of solutions to the heat equation},
journal = {Comptes Rendus. Math\'ematique},
pages = {761--768},
publisher = {Acad\'emie des sciences, Paris},
volume = {362},
year = {2024},
doi = {10.5802/crmath.593},
language = {en},
}
Pascal Auscher; Hedong Hou. On representation of solutions to the heat equation. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 761-768. doi : 10.5802/crmath.593. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.593/
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