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

• Published in: Comptes rendus. Mathématique Vol. 361; no. G9; pp. 1521 - 1530
• Main Authors: Burman, Erik, Delay, Guillaume, Ern, Alexandre, Oksanen, Lauri
• Format: Journal Article
• Language: English
• Published: Académie des sciences (Paris) 01.01.2023; Académie des sciences
• Subjects: Analysis of PDEs; Mathematics

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...