Quantification of the unique continuation property for the heat equation

Laurent Bourgeois

doi:10.3934/mcrf.2017012

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2017, Volume 7, Issue 3: 347-367. Doi: 10.3934/mcrf.2017012

This issue Previous Article Next Article Boundary feedback stabilization of the monodomain equations

Quantification of the unique continuation property for the heat equation

Laurent Bourgeois

Laboratoire POEMS, Ensta ParisTech, 828 Boulevard des Maréchaux, 91120 Palaiseau, France

Received: March 31, 2016

Revised: October 31, 2016

Published: October 2017

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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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Mathematics Subject Classification: Primary: 35R25, 35K05; Secondary: 35R30.

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