Erik Burman, Guillaume Delay, Alexandre Ern, Lauri Oksanen
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引用次数: 0
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.
期刊介绍：
The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, …
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