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Unique continuation from Cauchy data in unknown non-smooth domains

Luca Rondi (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We consider a conducting body which presents some (unknown) perfectly insulating defects, such as cracks or cavities, for instance. We perform measurements of current and voltage type on a (known) part of the boundary of the conductor. We prove that, even if the defects are unknown, the current and voltage measurements at the boundary uniquely determine the corresponding electrostatic potential inside the conductor. A corresponding stability result, related to the stability of Neumann problems with...

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...

Currently displaying 261 – 280 of 355