Quantification of the unique continuation property for the heat equation | Zendy

Laurent Bourgeois | Zendy

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Quantification of the unique continuation property for the heat equation

Author(s) -

Laurent Bourgeois

Publication year - 2017

Publication title -

mathematical control and related fields

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.658

H-Index - 21

eISSN - 2156-8472

pISSN - 2156-8499

DOI - 10.3934/mcrf.2017012

Subject(s) - logarithm , heat equation , continuation , mathematics , stability (learning theory) , exponent , domain (mathematical analysis) , cauchy distribution , initial value problem , property (philosophy) , convergence (economics) , term (time) , mathematical analysis , cauchy problem , computer science , physics , linguistics , philosophy , epistemology , quantum mechanics , machine learning , economics , programming language , economic growth

International audienceIn 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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