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Carleman estimates for the non-stationary Lamé system and the application to an inverse problem

Oleg Yu. Imanuvilov, Masahiro Yamamoto (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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 ) × ω , where T > 0 is a sufficiently large time interval and a subdomain ω satisfies a non-trapping condition.

Carleman estimates for the non-stationary Lamé system and the application to an inverse problem

Oleg Yu. Imanuvilov, Masahiro Yamamoto (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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.

Carleman estimates with two large parameters for second order operators and applications to elasticity with residual stress

Victor Isakov, Nanhee Kim (2008)

Applicationes Mathematicae

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"...

Crack detection using electrostatic measurements

Martin Brühl, Martin Hanke, Michael Pidcock (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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...

Crack detection using electrostatic measurements

Martin Brühl, Martin Hanke, Michael Pidcock (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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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