Аннотация:

We study the multidimensional initial-boundary value problem for the system of Kelvin--Voigt equations of a two-component mixture of viscoelastic fluids with nonlinear convective terms and a linear impulsive term --- a regular minor term describing impulsive source or damping. The impulsive term depends on a positive integer parameter $n$ and, as $n\to +\infty$, weakly$^\star$ converges to an expression including the Dirac delta-function, which models impulsive source or damping at the initial moment of time. We prove that an infinitesimal initial impulsive layer, associated with the Dirac delta function, is formed as $n\to+\infty$, and that the family of regular weak solutions to the original problem converges to the strong solution of a two-scale microscopic-macroscopic model. This model consists of two initial-boundary value problems that should be solved successively: at first, the flow of the mixture is defined on the infinitesimal initial impulsive layer set at the microscopic (`fast') timescale, and, at second, the outer flow beyond the initial impulsive layer is defined at the macroscopic (`slow') timescale. The equations of the initial impulsive layer inherit the full information about the profile of the original non-instantaneous source or damping.