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We establish a Carleman type inequality for the subelliptic operator in , , where , . As a consequence, we show that has the strong unique continuation property at points of the degeneracy manifold if the potential is locally in certain spaces.
In this paper, we establish Carleman estimates for the two dimensional isotropic non-stationary Lamé system with the zero Dirichlet boundary conditions. Using this estimate, we prove the uniqueness and the stability in determining spatially varying density and two Lamé coefficients by a single measurement of solution over , where is a sufficiently large time interval and a subdomain satisfies a non-trapping condition.
In this paper, we establish Carleman estimates for the two
dimensional isotropic non-stationary Lamé system with the zero Dirichlet boundary
conditions. Using this estimate, we prove the uniqueness and the
stability in determining spatially varying density and two Lamé
coefficients by a single measurement of solution over (0,T) x ω, where T > 0 is a sufficiently large time interval and a subdomain
ω satisfies a non-trapping condition.
We derive Carleman type estimates with two large parameters for a general partial differential operator of second order. The weight function is assumed to be pseudo-convex with respect to the operator. We give applications to uniqueness and stability of the continuation of solutions and identification of coefficients for the Lamé system of dynamical elasticity with residual stress. This system is anisotropic and cannot be principally diagonalized, but it can be transformed into an "upper triangular"...
A necessary and sufficient condition for the continuous extendibility of a solution of the Neumann problem for the Laplace equation is given.
We consider a controllability problem for a beam, clamped at one boundary and
free at the other boundary, with an attached piezoelectric actuator. By
Hilbert Uniqueness Method (HUM)
and new results on diophantine approximations, we
prove that the space of exactly initial controllable data depends on the
location of the actuator. We also illustrate these results with numerical
simulations.
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