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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.

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