On properties of solution of a boundary value problem describing simultaneous flow of two binary mixtures

Properties of an invariant solution of thermodiffusion equations in a planar layer are investigated in the case when the surface tension on the surface of two mixtures depends linearly on temperature and concentration. For the arising adjoint initial-boundary value problem, a priori estimates of perturbations of velocity and temperature fields are obtained. The estimates show that perturbations converge exponentially to stationary values as time increases. Concentration perturbations also settle into a stationary regime; this is proved by means of the Laplace transformation.