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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, a) is the given thermal flux for (t,σ) ∈ (0,T) x A, and that the corresponding output datum is the temperature u(T 0 , a) measured at a given time To for a E A o u t C 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 o u t ). The same result holds when a mean value of the temperature is measured over a small interval of time.

Unique Localization of Unknown Boundaries in a Conducting Medium from Boundary Measurements