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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"...
In this paper we extend recent work on the detection of inclusions using electrostatic measurements to the problem of crack detection in a two-dimensional object. As in the inclusion case our method is based on a factorization of the difference between two Neumann-Dirichlet operators. The factorization possible in the case of cracks is much simpler than that for inclusions and the analysis is greatly simplified. However, the directional information carried by the crack makes the practical implementation...
In this paper we extend recent work on the detection of inclusions
using electrostatic measurements to the problem of crack detection
in a two-dimensional object. As in the inclusion case our method is
based on a factorization of the difference between two
Neumann-Dirichlet operators. The factorization possible in the case
of cracks is much simpler than that for inclusions and the analysis
is greatly simplified. However, the directional information carried
by the crack makes the practical...
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