On Dynamics of Viscoelastic Multidimensional Medium with Variable Boundary

Here V(t,x) = (V1, . . . ,Vn), ρ(t,x) are a vector function and a scalar function which denote the velocity and the density of the medium, G(Z) is an n×n matrix function with the coefficients gi j = gi j(z11, . . . , znn) whose arguments are the coefficients of an n× n matrix Z, Φ is a scalar function, G and Φ are supposed to be smooth, μ > 0. Next, B(V) = zx(0, t,x), where z(τ, t,x) is a solution to the Cauchy problem (in the integral form)