One-dimensional inverse coefficient problems of anisotropic viscoelasticity

Abstract

We consider the problem of finding the moduli of elasticity c11(x3), c12(x3), c44(x3), x3 > 0, occurring in the system of integrodifferential viscoelasticity equations for gomogenious anisotropic medium. The density of medium is contant. The matrix kernel k(t) = diag(k1, k2, k3)(t), t ∈ [0, T ] is known. As additional information is the Fourier transform of the first and third component of the displacements vector for x3 = 0. The results are the theorems on the existence of a unique solution of the inverse problems and the theorems of stability.