Properties of an Aggregated Quasi-Gasdynamic System
of Equations for a Homogeneous Gas Mixture
A. A. Zlotnika,b,* and A. S. Fedchenkoa,**
a Higher School of Economics University,
Moscow, 109028 Russia
b Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences,
Moscow, 125047 Russia
Correspondence to: *e-mail: azlotnik@hse.ru
Correspondence to: **e-mail: asfedchenko@yandex.ru
Received 27 May, 2021
Abstract—For an aggregated quasi-gasdynamic system of equations for a homogeneous gas mixture, we give an entropy balance equation with a nonnegative entropy production in the presence of diffusion fluxes. We also derive the existence, uniqueness, and L2-dissipativity of weak solutions to an initial-boundary value problem for the system linearized at a constant solution. Additionally, the Petrovskii parabolicity and local-in-time classical unique solvability of the Cauchy problem for the quasi-gasdynamic system itself are established.
Keywords: quasi-gasdynamic system of equations, homogeneous gas mixture, entropy balance equation, Petrovskii parabolicity, L2-dissipativity
DOI: 10.1134/S1064562421060193