Unique localization of unknown boundaries in a conducting medium from boundary measurements
ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 1-22.

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)×A, and that the corresponding output datum is the temperature u(T 0 ,σ) measured at a given time T 0 for σA out A, we prove that I and D are uniquely localized from knowledge of all possible pairs of input-output data (g,u(T 0 ) A out ). The same result holds when a mean value of the temperature is measured over a small interval of time.

DOI : 10.1051/cocv:2002001
Classification : 35R30
Mots clés : inverse boundary value problems, cavities, corrosion, uniqueness
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     title = {Unique localization of unknown boundaries in a conducting medium from boundary measurements},
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     publisher = {EDP-Sciences},
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     url = {http://archive.numdam.org/articles/10.1051/cocv:2002001/}
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Canuto, Bruno. Unique localization of unknown boundaries in a conducting medium from boundary measurements. ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 1-22. doi : 10.1051/cocv:2002001. http://archive.numdam.org/articles/10.1051/cocv:2002001/

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