Abstract: We study the multidimensional initial-boundary value problem for the system of Kelvin Voigt equations of a two-component mixture of viscoelastic uids 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 → +∞, weakly⋆ 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 in nitesimal initial impulsive layer, associated with the Dirac delta function, is formed as n → +∞, 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 rst, the ow of the mixture is de ned on the in nitesimal initial impulsive layer set at the microscopic (`fast') timescale, and, at second, the outer ow beyond the initial impulsive layer is de ned at the macroscopic (`slow') timescale. The equations of the initial impulsive layer inherit the full information about the pro le of the original non-instantaneous source or damping.

Cite: Antontsev S.N. , Kuznetsov I.V. , Prokudin D.A. , Sazhenkov S.A.
The impulsive Kelvin--Voigt equations for two-component mixtures of viscoelastic fluids
Сибирские электронные математические известия / Siberian Electronic Mathematical Reports. 2025. V.22. N1. P.563-586. DOI: 10.33048/semi.2025.22.038 WOS Scopus

Identifiers:

Web of science:	WOS:001525502900008
Scopus:	2-s2.0-105020441944

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