Burman, E;
Delay, G;
Ern, A;
Oksanen, L;
(2023)
A stability estimate for data assimilation subject to the heat equation with initial datum.
Comptes Rendus Mathematique
, 361
pp. 1521-1530.
10.5802/CRMATH.506.
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Abstract
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.
| Type: | Article |
|---|---|
| Title: | A stability estimate for data assimilation subject to the heat equation with initial datum |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.5802/CRMATH.506 |
| Publisher version: | https://doi.org/10.5802/crmath.506 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10184756 |
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