On the determination of the coefficients in the viscoelasticity equations

For the integrodifferential viscoelasticity equations, we study the problem of determining the coefficients of the equations and the kernels occurring in the integral terms of the system of equations. The density of the medium is assumed to be given. We suppose that the inhomogeneity support of the sought functions is included in some compact domain $B_0$. We consider a series of inverse problems in which an impulse source is concentrated at the points $y$ of the boundary of $B_0$. The point y is the parameter of the problem. The given information about the solution is the trace of the solution to the Cauchy problem with zero initial data. This trace is given on the boundary of $B_0$ for all $y\in\partial B_0$ and for a finite time interval. The main result of the article consists in obtaining uniqueness theorems for a solution to the initial inverse problem.