Two-Dimensional Inverse Problem for a Viscoelasticity Equationin a Vertically Inhomogeneous Medium

The two-dimensional inverse problem of determining the kernel of an elasticity equation of memory type is studied. It is assumed that the coefficients of the equations depend on only one spatial variable. Applying the linearization principle, the inverse problem is reduced to an equivalent linear system of integral equations. The generalized principle of compressed maps is applied to the latter in the space of continuous functions. The theorem of unique solvability is proved and an estimate of the stability of the solution to the inverse problem is obtained.