One-dimensional inverse coefficient problems of anisotropic viscoelasticity

We consider the problem of finding the moduli of elasticity $c_{11}(x_3), c_{12}(x_3), c_{44}(x_3)$, $x_3>0$, occurring in the system of integro-differential viscoelasticity equations for gomogenious anisotropic medium. The density of medium is contant. The matrix kernel $k(t)=diag(k_1,$ $k_2,$ $k_3)(t),$ $t\in [0,T]$ is known. As additional information is the Fourier transform of the first and third component of the displacements vector for $x_3 = 0$. The results are the theorems on the existence of a unique solution of the inverse problems and the theorems of stability.