An Inverse Problem for a Dynamical Lamé System with Residual Stress

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, Lamé 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 Lamé system possesses a suitable pseudoconvex function, residual stress is small, and three sets of the initial data satisfy some independency condition.