An inverse problem for the system of viscoelasticity equations in homogeneous anisotropic media

Under study is the problem of reconstructing the memory function of a viscoelastic medium from the system of viscoelastic equations for a homogeneous anisotropic medium. As additional information, the Fourier image of the displacement vector with respect to the spatial variables for the values $\nu_0\neq 0$ of the transformation parameter is given. It is demonstrated that, provided the data of the problem satisfy some conditions of agreement and smoothness, the solution of the problem is uniquely determined in the class of continuous functions and depends continuously on the given functions.