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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...

Weak solutions to a time-dependent heat equation with nonlocal radiation boundary condition and arbitrary p -summable right-hand side

Pierre-Etienne Druet (2010)

Applications of Mathematics

We consider a model for transient conductive-radiative heat transfer in grey materials. Since the domain contains an enclosed cavity, nonlocal radiation boundary conditions for the conductive heat-flux are taken into account. We generalize known existence and uniqueness results to the practically relevant case of lower integrable heat-sources, and of nonsmooth interfaces. We obtain energy estimates that involve only the L p norm of the heat sources for exponents p close to one. Such estimates are...

Wentzell Boundary Conditions in the Nonsymmetric Case

A. Favini, G. R. Goldstein, J. A. Goldstein, S. Romanelli (2008)

Mathematical Modelling of Natural Phenomena

Let L be a nonsymmetric second order uniformly elliptic operator with generalWentzell boundary conditions. We show that a suitable version of L generates a quasicontractive semigroup on an Lp space that incorporates both the underlying domain and its boundary. This extends the earlier work of the authors on the symmetric case.

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