Asymptotic representation of the solution of the problem of the propagation of acoustic waves in a non-uniform compressible relaxing medium

An equation describing the propagation of non-stationary acoustic waves in a non-uniform compressible relaxing medium is derived. The problem of the existence and uniqueness of a solution of the first initialboundary value problem for this equation is studied. The first term of the asymptotic expansion of the solution with respect to a small parameter multiplying the operator of the highest order in the equation is constructed.