[Sur la représentation des solutions de l’équation de la chaleur]
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 .
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.
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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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