Existence and uniqueness of the solution of the initial-boundary value problem for one-dimensional equations of the dynamics of a compressible viscous mixture

V. Yu. Nogovishcheva^a, D. A. Prokudin<sup>bc

a</sup> Novosibirsk State University, Novosibirsk, Russia
^b Lavrentyev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
^c Altai State University, Barnaul, Russia

Abstract: In this paper, an initial-boundary value problem is studied for one-dimensional equations of the dynamics of a compressible viscous mixture. A theorem is proved for the existence and uniqueness of a solution to the initial-boundary value problem without any restrictions on the structure of the viscosity matrix other than the standard physical requirements of symmetry and positive definiteness.

Keywords: dynamics of a compressible viscous mixture, one-dimensional initial-boundary value problem, off-diagonal viscosity matrix, existence and uniqueness of a solution.

UDC: 517.95

DOI: 10.22363/2413-3639-2025-71-3-395-416