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

Oleg Yu. Imanuvilov; Masahiro Yamamoto

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 11, Issue: 1, page 1-56
  • ISSN: 1292-8119

Abstract

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

How to cite

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Imanuvilov, Oleg Yu., and Yamamoto, Masahiro. "Carleman estimates for the non-stationary Lamé system and the application to an inverse problem." ESAIM: Control, Optimisation and Calculus of Variations 11.1 (2010): 1-56. <http://eudml.org/doc/90755>.

@article{Imanuvilov2010,
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. },
author = {Imanuvilov, Oleg Yu., Yamamoto, Masahiro},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Carleman estimate; Lamé system; inverse problem.; uniqueness; stability; Lamé coefficients},
language = {eng},
month = {3},
number = {1},
pages = {1-56},
publisher = {EDP Sciences},
title = {Carleman estimates for the non-stationary Lamé system and the application to an inverse problem},
url = {http://eudml.org/doc/90755},
volume = {11},
year = {2010},
}

TY - JOUR
AU - Imanuvilov, Oleg Yu.
AU - Yamamoto, Masahiro
TI - Carleman estimates for the non-stationary Lamé system and the application to an inverse problem
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 11
IS - 1
SP - 1
EP - 56
AB - 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.
LA - eng
KW - Carleman estimate; Lamé system; inverse problem.; uniqueness; stability; Lamé coefficients
UR - http://eudml.org/doc/90755
ER -

References

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