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Quantification of the unique continuation property for the heat equation

Laurent Bourgeois 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
Abstract : In this paper we prove a logarithmic stability estimate in the whole domain for the solution to the heat equation with a source term and lateral Cauchy data. We also prove its optimality up to the exponent of the logarithm and show an application to the identification of the initial condition and to the convergence rate of the quasi-reversibility method.
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Laurent Bourgeois. Quantification of the unique continuation property for the heat equation. Mathematical Control and Related Fields, AIMS, 2017, 7 (3), pp.347 - 367. ⟨10.3934/mcrf.2017012⟩. ⟨hal-01648045⟩

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