The problem on small motions of a mixture of viscous compressible fluids

Abstract

In this paper, we study the problem on small motions and normal oscillations of a homogeneous mixture of several viscous compressible fluids filling a bounded domain of three-dimensional space with an infinitely smooth boundary. The boundary condition of slippage without shear stresses is considered. It is proved that the essential spectrum of the problem is a finite set of segments located on the real axis. The discrete spectrum lies on the real axis, with the possible exception of a finite number of complex conjugate eigenvalues. The spectrum of the problem contains a subsequence of eigenvalues with a limit point
at infinity and a power-law asymptotic distribution. The asymptotic behavior of solutions to the evolution problem is studied.