On representation of solutions to the heat equation
We propose a simple method to obtain semigroup representation of solutions to the heat equation using a local $L^2$ 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...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-09-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.593/ |
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| _version_ | 1825206210711781376 |
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| author | Auscher, Pascal Hou, Hedong |
| author_facet | Auscher, Pascal Hou, Hedong |
| author_sort | Auscher, Pascal |
| collection | DOAJ |
| description | We propose a simple method to obtain semigroup representation of solutions to the heat equation using a local $L^2$ 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 $\operatorname{BMO}^{-1}$ initial data. |
| format | Article |
| id | doaj-art-1be45eebe42541b29f9aaba89cb05e64 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-1be45eebe42541b29f9aaba89cb05e642025-02-07T11:22:28ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-09-01362G776176810.5802/crmath.59310.5802/crmath.593On representation of solutions to the heat equationAuscher, Pascal0Hou, Hedong1https://orcid.org/0000-0002-2810-4480Université Paris-Saclay, CNRS, Laboratoire de Mathématiques d’Orsay, 91405 Orsay, FranceUniversité Paris-Saclay, CNRS, Laboratoire de Mathématiques d’Orsay, 91405 Orsay, FranceWe propose a simple method to obtain semigroup representation of solutions to the heat equation using a local $L^2$ 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 $\operatorname{BMO}^{-1}$ initial data.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.593/ |
| spellingShingle | Auscher, Pascal Hou, Hedong On representation of solutions to the heat equation Comptes Rendus. Mathématique |
| title | On representation of solutions to the heat equation |
| title_full | On representation of solutions to the heat equation |
| title_fullStr | On representation of solutions to the heat equation |
| title_full_unstemmed | On representation of solutions to the heat equation |
| title_short | On representation of solutions to the heat equation |
| title_sort | on representation of solutions to the heat equation |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.593/ |
| work_keys_str_mv | AT auscherpascal onrepresentationofsolutionstotheheatequation AT houhedong onrepresentationofsolutionstotheheatequation |