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KIAM Preprint № 77, Moscow, 2021
Authors: Zlotnik A.A., Fedchenko A.S.
Properties of the aggregated quasi-hydrodynamic system of equations for a homogeneous gas mixture with a common regularizing velocity
Abstract:
We study a quasi-hydrodynamic system of equations for a homogeneous (with common velocity and temperature) multicomponent gas mixture in the absence of chemical reactions, with a regularizing velocity common for the components. We derive the entropy balance equation with a non-negative entropy production taking into account the diffusion fluxes of the mixture components. In the absence of diffusion fluxes, a system of equations linearized at a constant solution is constructed by a new technique, In the absence of diffusion fluxes, a system of equations linearized on a constant solution is constructed by a new technique. It is reduced to a symmetric form, the L2-dissipativity of its solutions is proved, and a degeneration (with respect to the densities of the mixture components) of the parabolicity property for the original system is established. Actually, the system has the composite type. The obtained properties strictly reflect its physical correctness and dissipative nature of the quasi-hydrodynamic regularization.
Keywords:
homogeneous gas mixture, quasi-hydrodynamic system of equations, entropy balance equation, linearization, dissipativity, parabolicity
Publication language: russian,  pages: 26
Research direction:
Theoretical and applied problems of mechanics
Russian source text:
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About authors:
  • Zlotnik Alexander Anatolievich,  orcid.org/0000-0003-2440-2816,  Higher School of Economics University; KIAM RAS
  • Fedchenko Anna Sergeevna,  orcid.org/0000-0002-9450-3498,  Higher School of Economics University