A stability estimate for data assimilation subject to the heat equation with initial datum
This paper studies the unique continuation problem for the heat equation. We prove a so-called conditional stability estimate for the solution. We are interested in local estimates that are Hölder stable with the weakest possible norms of data on the right-hand side. Such an estimate is useful for t...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2023-11-01
|
| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.506/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1825206243184082944 |
|---|---|
| author | Burman, Erik Delay, Guillaume Ern, Alexandre Oksanen, Lauri |
| author_facet | Burman, Erik Delay, Guillaume Ern, Alexandre Oksanen, Lauri |
| author_sort | Burman, Erik |
| collection | DOAJ |
| description | This paper studies the unique continuation problem for the heat equation. We prove a so-called conditional stability estimate for the solution. We are interested in local estimates that are Hölder stable with the weakest possible norms of data on the right-hand side. Such an estimate is useful for the convergence analysis of computational methods dealing with data assimilation. We focus on the case of a known solution at initial time and in some subdomain but that is unknown on the boundary. To the best of our knowledge, this situation has not yet been studied in the literature. |
| format | Article |
| id | doaj-art-82abfb8bd3ad43f28b163b5819686067 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-82abfb8bd3ad43f28b163b58196860672025-02-07T11:10:50ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-11-01361G91521153010.5802/crmath.50610.5802/crmath.506A stability estimate for data assimilation subject to the heat equation with initial datumBurman, Erik0Delay, Guillaume1https://orcid.org/0000-0002-3624-7422Ern, Alexandre2Oksanen, Lauri3Department of Mathematics, University College London, London, UK–WC1E 6BT, UKSorbonne Université, CNRS, Université Paris Cité, LJLL, F-75005 Paris, FranceCERMICS, École des Ponts, 77455 Marne-la-Vallée cedex 2, and INRIA, Paris, FranceUniversity of Helsinki, Department of Mathematics and Statistics, P.O 68, 00014 University of Helsinki, FinlandThis paper studies the unique continuation problem for the heat equation. We prove a so-called conditional stability estimate for the solution. We are interested in local estimates that are Hölder stable with the weakest possible norms of data on the right-hand side. Such an estimate is useful for the convergence analysis of computational methods dealing with data assimilation. We focus on the case of a known solution at initial time and in some subdomain but that is unknown on the boundary. To the best of our knowledge, this situation has not yet been studied in the literature.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.506/ |
| spellingShingle | Burman, Erik Delay, Guillaume Ern, Alexandre Oksanen, Lauri A stability estimate for data assimilation subject to the heat equation with initial datum Comptes Rendus. Mathématique |
| title | A stability estimate for data assimilation subject to the heat equation with initial datum |
| title_full | A stability estimate for data assimilation subject to the heat equation with initial datum |
| title_fullStr | A stability estimate for data assimilation subject to the heat equation with initial datum |
| title_full_unstemmed | A stability estimate for data assimilation subject to the heat equation with initial datum |
| title_short | A stability estimate for data assimilation subject to the heat equation with initial datum |
| title_sort | stability estimate for data assimilation subject to the heat equation with initial datum |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.506/ |
| work_keys_str_mv | AT burmanerik astabilityestimatefordataassimilationsubjecttotheheatequationwithinitialdatum AT delayguillaume astabilityestimatefordataassimilationsubjecttotheheatequationwithinitialdatum AT ernalexandre astabilityestimatefordataassimilationsubjecttotheheatequationwithinitialdatum AT oksanenlauri astabilityestimatefordataassimilationsubjecttotheheatequationwithinitialdatum AT burmanerik stabilityestimatefordataassimilationsubjecttotheheatequationwithinitialdatum AT delayguillaume stabilityestimatefordataassimilationsubjecttotheheatequationwithinitialdatum AT ernalexandre stabilityestimatefordataassimilationsubjecttotheheatequationwithinitialdatum AT oksanenlauri stabilityestimatefordataassimilationsubjecttotheheatequationwithinitialdatum |