THE LINEARIZATION OF INVERSE SPECTRAL PROBLEMS FOR NONHOMOGENEOUS ELASTIC BODIES

The goal of this paper is to formulate inverse spectral problems for t he determination of a multidimensional distribution of moduli of elast icity and density in nonhomogeneous materials, as well as to develop c onstructive methods for their solution. Our treatment of the problems starts with the linearized inverse spectral Sturm-Liouville problem, w hich can be reduced to an integral Fredholm equation of the first kind with the property of stability. Then we formulate the operator approa ch to these problems, based on the method of indirect influence combin ed with linearization. The use of these methods within the framework o f linear elasticity allows the determination of sufficient information for the solution of inverse problems in a nonhomogeneous anisotropic subdomain of an elastic body.