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We consider the problem of localizing an inaccessible piece of the boundary of a conducting medium , and a cavity contained in , from boundary measurements on the accessible part of . Assuming that is the given thermal flux for , and that the corresponding output datum is the temperature measured at a given time for , we prove that and are uniquely localized from knowledge of all possible pairs of input-output data . The same result holds when a mean value of the temperature...
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 . The same
result...
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