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...

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Bibliographic Details
Published inComptes rendus. Mathématique Vol. 361; no. G9; pp. 1521 - 1530
Main Authors Burman, Erik, Delay, Guillaume, Ern, Alexandre, Oksanen, Lauri
Format Journal Article
LanguageEnglish
Published Académie des sciences (Paris) 01.01.2023
Académie des sciences
Subjects
Analysis of PDEs
Mathematics
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Summary: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.
ISSN:1778-3569
1631-073X
1778-3569
DOI:10.5802/crmath.506