Quantification of the unique continuation property for the heat equation

Laurent Bourgeois

doi:10.3934/mcrf.2017012

Quantification of the unique continuation property for the heat equation

Laurent Bourgeois

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	347-367
Number of pages	21
Journal	Mathematical Control and Related Fields
Volume	7
Issue number	3
DOIs	https://doi.org/10.3934/mcrf.2017012
Publication status	Published - 1 Sept 2017

Keywords

Carleman estimate
Distance function
Heat equation
Lateral Cauchy data
Stability estimate

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title = "Quantification of the unique continuation property for the heat equation",

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.",

keywords = "Carleman estimate, Distance function, Heat equation, Lateral Cauchy data, Stability estimate",

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N2 - 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.

AB - 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.

KW - Carleman estimate

KW - Distance function

KW - Heat equation

KW - Lateral Cauchy data

KW - Stability estimate

UR - https://www.scopus.com/pages/publications/85021914547

U2 - 10.3934/mcrf.2017012

DO - 10.3934/mcrf.2017012

M3 - Article

AN - SCOPUS:85021914547

SN - 2156-8472

VL - 7

SP - 347

EP - 367

JO - Mathematical Control and Related Fields

JF - Mathematical Control and Related Fields

IS - 3

ER -

Quantification of the unique continuation property for the heat equation

Abstract

Keywords

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