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Article Dans Une Revue Comptes Rendus. Mathématique Année : 2024

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

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.
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Dates et versions

hal-03830744 , version 1 (26-10-2022)
hal-03830744 , version 2 (13-04-2023)
hal-03830744 , version 3 (07-11-2023)

Identifiants

Citer

Erik Burman, Guillaume Delay, Alexandre Ern, Lauri Oksanen. A stability estimate for data assimilation subject to the heat equation with initial datum. Comptes Rendus. Mathématique, inPress, 361 (G9), pp.1521-1530. ⟨10.5802/crmath.506⟩. ⟨hal-03830744v3⟩
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