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Unique localization of unknown boundaries in a conducting medium from boundary measurements

Bruno Canuto (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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 σ A 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...

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

Bruno Canuto (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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 ) A out ) . The same result...

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