On the properties of a quasihydrodynamic system of equations for a homogeneous gas mixture with a common regularizing velocity

Differential Equations. 2022. Vol. 58. No. 3. P. 341–356.

Zlotnik A.A., Fedchenko A.S.

We study a quasihydrodynamic system of equations for a homogeneous (with common velocity and temperature) multicomponent gas mixture in the absence of chemical reactions with a common regularizing velocity. For this system, we derive an entropy balance equation with nonnegative entropy production in the presence of diffusion flows of the mixture components. In the absence of diffusion flows, a system of equations linearized on a constant solution is constructed in a new way. This system is reduced to a symmetric form, the L^2-dissipativity of its solutions is proved, and the degeneracy (with respect to the densities of the mixture components) of the parabolic property of the original system is established. In fact, the system under study has a composite type. The obtained properties mathematically rigorously reflect its physical well-posedness and the dissipative nature of quasihydrodynamic regularization.

Keywords: quasi-hydrodynamic system of equations, L^2-dissipativity, homogeneous gas mixture, entropy balance equation, linearized system of equations, parabolicity