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Unique Localization of Unknown Boundariesin a Conducting Medium from Boundary Measurements

Published online by Cambridge University Press:  15 September 2002

Bruno Canuto
Bruno Canuto*
Affiliation:
Laboratoire de Mathématiques Appliquées, UMR 7641, Université de Versailles, 45 avenue des États-Unis, 78035 Versailles Cedex, France; canuto@math.uvsq.fr.
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Abstract

We consider the problem of localizing aninaccessible piece I of the boundary of a conducting medium Ω, anda cavity D contained in Ω, from boundary measurements on theaccessible part A of ∂Ω. Assuming that g(t,σ) isthe given thermal flux for (t,σ) ∈ (0,T) x A, andthat the corresponding output datum is the temperature u(T 0,σ)measured at a given time T 0 for σ ∈ A out ⊂ A, weprove that I and D are uniquely localized from knowledge of all possiblepairs of input-output data $(g,u(T_0)_{\mid A_{{\rm out}}})$ . The sameresult holds when a mean value of the temperature is measured over a smallinterval of time.

Keywords

Inverse boundary value problemscavitiescorrosionuniqueness.

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 7 , 2002 , pp. 1 - 22
Copyright
© EDP Sciences, SMAI, 2002

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