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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...
In this paper we prove a unique continuation
result for a cascade system of parabolic equations, in which the solution of the first
equation is (partially) used as a forcing term for the second equation. As a
consequence we prove the existence of ε-insensitizing controls for some
parabolic equations when the control region and the observability region do not intersect.
We study a non standard unique continuation property for the biharmonic spectral problem in a 2D corner with homogeneous Dirichlet boundary conditions and a supplementary third order boundary condition on one side of the corner. We prove that if the corner has an angle , and , a unique continuation property holds. Approximate controllability of a 2-D linear fluid-structure problem follows from this property, with a control acting on the elastic side of a corner in a domain containing a Stokes...
We study a non standard unique continuation property for the
biharmonic spectral problem in a 2D
corner with homogeneous Dirichlet boundary conditions and a
supplementary third order boundary condition on one side of the
corner. We prove that if the corner has an angle ,
and , a unique continuation
property holds. Approximate controllability of a 2-D linear
fluid-structure problem follows from this property, with a control
acting on the elastic side of a corner in a domain containing...
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