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

Abstract

In this paper, we establish Carleman estimates for the two dimensional isotropic nonstationary 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. © 2005 EDP Sciences, SMAI.