A. A. Zlotnik, A. S. Fedchenko, “Properties of an aggregated quasi-gasdynamic system of equations for a homogeneous gas mixture”, Dokl. RAN. Math. Inf. Proc. Upr., 2021, Volume 501,Pages <nobr>31

This article is cited in 4 papers

MATHEMATICS

Properties of an aggregated quasi-gasdynamic system of equations for a homogeneous gas mixture

A. A. Zlotnik^ab, A. S. Fedchenko^a

^a National Research University "Higher School of Economics", Moscow, Russia
^b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow, Russia

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 $L^2$-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, $L^2$-dissipativity.

UDC: 517.958:531.332

Presented: B. N. Chetverushkin
Received: 27.05.2021
Revised: 28.09.2021
Accepted: 29.09.2021

DOI: 10.31857/S2686954321060199