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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 of the boundary of a conducting medium Ω, and a cavity contained in Ω, from boundary measurements on the accessible part of ∂Ω. Assuming that is the given thermal flux for (,σ) ∈ (0,) x A, and that the corresponding output datum is the temperature ,σ) measured at a given time for σ ∈ ⊂ , we prove that and are uniquely localized from knowledge of all possible pairs of input-output...

Determining two coefficients in elliptic operators via boundary spectral data: a uniqueness result

Bruno CanutoOtared Kavian — 2004

Bollettino dell'Unione Matematica Italiana

For a bounded and sufficiently smooth domain Ω in R N , N 2 , let λ k k = 1 and φ k k = 1 be respectively the eigenvalues and the corresponding eigenfunctions of the problem (with Neumann boundary conditions) - div a x φ k + q x φ k = λ k ϱ x φ k  in  Ω , a n φ k = 0  su  Ω . We prove that knowledge of the Dirichlet boundary spectral data λ k k = 1 , φ k | Ω k = 1 determines uniquely the Neumann-to-Dirichlet (or the Steklov- Poincaré) map γ for a related elliptic problem. Under suitable hypothesis on the coefficients a , q , ϱ their identifiability is then proved. We prove also analogous results for Dirichlet...

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