The multidimensional problem of determining the density function for the system of viscoelasticity

The integro-differential system of viscoelasticity equations is considered. The problem of determining the function of density $\rho(x_2,x_3)$ is investigated. For its determination an additional condition relative to the Fourier transform of the first component of the displacements vector for $x_3 = 0$ is given. The theorems of the local unique solvability of the inverse problem is proved in the special class of functions. The stability estimate of solving the inverse problem is obtained.