On the Cauchy problem in the theory of coefficient inverse problems for elastic bodies

The inverse problems on the identification of inhomogeneous material properties of an elastic plate is considered. The condition of uniqueness of the inverse problems statements are analyzed. Direct problem on finding displacements to formulate the additional input data of the inverse problem is investigated; the accuracy of the direct problem solution is estimated by means of comparison with finite-element computation. A scheme of the inverse problem solving is proposed based on the application of the weak statement of the initial boundary problem and the projection method. A series of computation experiments on a reconstruction of various types of inhomogeneity laws of the Lamé coefficients is performed.