An inverse problem for a dynamical Lamé system with residual stress
Isakov, Victor, 1947-
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Isakov, Victor. 2007. An inverse problem for a dynamical Lamé system with residual stress. SIAM Journal on Mathematical Analysis.
In this paper we prove a Hölder and Lipschitz stability estimates of determining all coefficients of a dynamical Lamé system with residual stress, including the density, Lam´e parameters, and the residual stress, by three pairs of observations from the whole boundary or from a part of it. These estimates imply first uniqueness results for determination of all parameters in the residual stress systems from few boundary measurements. Our essential assumptions are that the Lam´e system possesses a suitable pseudoconvex function, residual stress is small, and three sets of the initial data satisfy some independency condition.
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