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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 continuation principle for systems of parabolic equations

Otared Kavian, Luz de Teresa (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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.

Unique continuation property near a corner and its fluid-structure controllability consequences

Axel Osses, Jean-Pierre Puel (2009)

ESAIM: Control, Optimisation and Calculus of Variations

We study a non standard unique continuation property for the biharmonic spectral problem Δ 2 w = - λ Δ w 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 0 < θ 0 < 2 π , θ 0 ≠ π and θ 0 ≠ 3 π / 2 , 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...

Unique continuation property near a corner and its fluid-structure controllability consequences

Axel Osses, Jean-Pierre Puel (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We study a non standard unique continuation property for the biharmonic spectral problem Δ 2 w = - λ Δ w 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 0 < θ 0 < 2 π , θ 0 ≠ π and θ 0 ≠ 3 π / 2 , 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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