A stability estimate for data assimilation subject to the heat equation with initial datum

Erik Burman; Guillaume Delay; Alexandre Ern; Lauri Oksanen

doi:10.5802/CRMATH.506

A stability estimate for data assimilation subject to the heat equation with initial datum

Titre traduit de la contribution: Une estimée de stabilité pour l'assimilation de données pour l'équation de la chaleur avec une donnée initiale

Erik Burman
, Guillaume Delay
, Alexandre Ern
, Lauri Oksanen

Department of Mathematics
University College London
Sorbonne Université
Department of Mathematics and Statistics
University of Helsinki

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

Titre traduit de la contribution	Une estimée de stabilité pour l'assimilation de données pour l'équation de la chaleur avec une donnée initiale
langue originale	Anglais
Pages (de - à)	1521-1530
Nombre de pages	10
journal	Comptes Rendus Mathematique
Volume	361
Les DOIs	https://doi.org/10.5802/CRMATH.506
état	Publié - 1 janv. 2023

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AB - 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.

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A stability estimate for data assimilation subject to the heat equation with initial datum

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