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

Published online by Cambridge University Press:  15 December 2004

Oleg Yu. Imanuvilov  and
Masahiro Yamamoto
Oleg Yu. Imanuvilov
Affiliation:
Department of Mathematics, Iowa State University, 400 Carver Hall Ames IA 50011-2064 USA; vika@iastate.edu
Masahiro Yamamoto
Affiliation:
Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro Tokyo 153-8914 Japan; myama@ms.u-tokyo.ac.jp
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Abstract

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.

Keywords

Carleman estimateLamé systeminverse problem.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 1 , January 2005 , pp. 1 - 56
Copyright
© EDP Sciences, SMAI, 2005

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