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Unique Localization of Unknown Boundaries in 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 an inaccessible piece I of the boundary of a conducting medium Ω, and a cavity D contained in Ω, from boundary measurements on the accessible part A of ∂Ω. Assuming that g(t,σ) is the given thermal flux for (t,σ) ∈ (0,T) x A, and that the corresponding output datum is the temperature u(T0,σ) measured at a given time T0 for σ ∈ Aout ⊂ A, we prove that I and D are uniquely localized from knowledge of all possible pairs of input-output data $(g,u(T_0)_{\mid A_{{\rm out}}})$. The same result holds when a mean value of the temperature is measured over a small interval of time.

Keywords

Inverse boundary value problemscavitiescorrosionuniqueness.
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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