On the Stabilization of the Solution to the Initial Boundary Value Problem for One-Dimensional Isothermal Equations of Viscous Compressible Multicomponent Media Dynamics

Abstract

An initial boundary value problem is considered for one-dimensional isothermal equations of the dynamics of viscous compressible multicomponent media, which are a generalization of the Navier–Stokes equations. The stabilization of the solution to the initial boundary value problem is proven while the time tends to infinity, without simplifying assumptions for the structure of the viscosity matrix, except for the standard physical requirements of symmetry and positive definiteness. It is shown that the stabilization of the solution is exponential.