Un algorithme d'identification de frontières soumises à des conditions aux limites de Signorini
Un algorithme d'identification de frontières soumises à des conditions aux limites de Signorini
This work deals with a non linear inverse problem of reconstructing an unknown boundary γ, the boundary conditions prescribed on γ being of Signorini type, by using boundary measurements. The problem is turned into an optimal shape design one, by constructing a Kohn & Vogelius-like cost function, the only minimum of which is proved to be the unknown boundary. Furthermore, we prove that the derivative of this cost function with respect to a direction θ depends only on the state u0, and not...
Un problème de symétrie pour une équation biharmonique
Un problème inverse en formage des métaux liquides
Una equazione parabolica in teoria della combustione: problemi diretti ed inversi
Unique continuation from Cauchy data in unknown non-smooth domains
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
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...
Unique Localization of Unknown Boundaries in a Conducting Medium from Boundary Measurements
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...
Uniqueness for a boundary identification problem in thermal imaging.
Uniqueness in a one-dimensional problem of finding a time-dependent potential.
Uniqueness in an inverse problem for an elasticity system.
Uniqueness of semilinear elliptic inverse problem.
Uniqueness of the Multi-Dimensional Inverse Scattering Problem for Time Dependent Potentials.