Mixed Value Problem for a One-Dimensional Nonlinear Nonstationary Twelve moment BoltzmannS System Equations with the Maxwell-Auzhan Boundary Conditions

Authors

  • Sh. Akimzhanova

Boltzmann's homogeneous one-dimensional equation, Boltzmann’s moment system equations

Abstract

It is proved existence and uniqueness of solution of the problem with initial and boundary conditions of Maxwell-Auzhan (we consider pure specular reflection from the boundary) for the nonstationary nonlinear one-dimensional Boltzmann's twelve-moment system equations in space of functions continuous in time and summable in square by spatial variable.

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How to Cite

Mixed Value Problem for a One-Dimensional Nonlinear Nonstationary Twelve moment BoltzmannS System Equations with the Maxwell-Auzhan Boundary Conditions. (2020). Global Journal of Science Frontier Research, 20(F5), 37-47. https://www.journalofscience.org/index.php/GJSFR/article/view/2754

References

Auzhan Sakabekov, Yerkanat Auzhani (2014) Boundary conditions for the one-dimensional nonlinear nonstationary Boltzmann's moment system equations. 55(12), 123507.

Mikhail Kogan (1967) Rarefied Gas Dynamics. 440.

R Barantcev (1975) Gas-Surface Interaction: Tangential Momentum Accommodation Coefficients of Rare Gases on Polycrystalline Metal Surfaces. 531-538.

A Latyshev, A Yushkanov (2004) Moment Boundary Conditions in Rarefied Gas Slip-Flow Problems// Fluid Dynamics. 193-208.

Y Khlopkov, M Zeia, A Khlopkov (2014) Techniques for solving high-altitude tasks in a rarefied gas. (1), 156-162.

G Grad (1949) On the kinetic theory of rarefied gases. 2(4), 331-407.

G Grad (1958) Principles of the Kinetic Theory of Gases. 12, 205-294.

A Sakabekov (1994) Initial-boundary value problems for the Boltzmann's moment system equations in an arbitrary approximation. 77(1), 57-76.

C Cercignani (1975) Theory and application of the Boltzmann equation.

K Kumar (1966) Polynomial expansions in Kinetic theory of gases. 57, 115-141.

V Neudachin, U Smirnov (1969) Nucleon association of easy kernel.

M Moshinsky (1960) The harmonic oscillator in modern physics: from atoms to quarks. 152.

A Bobylev, S Rjasanow (1975) Numerical solution of the Boltzmann equation using a fully conservative difference scheme based on the fast fourier transform. 29(3-5), 289-310.

V Vedeniapin (1981) Anisotropic solutions of the nonlinear Boltzmann equation for Maxwellian molecule. 256, 338-342.

C Levermore (1996) Moment closure hierarchies for kinetic theories. 83(5-6), 1021-1065.

R Barantcev, M Lutcet (1969) About boundary condition for moment equations of rarefied gases. 92-101.

Stéphane Mischler (2010) Kinetic equations with Maxwell boundary conditions. 43(5), 719-760.

A Sakabekov, Y Auzhani (2014) Boundary conditions for the one dimensional nonlinear nonstationary Boltzmann's moment system equations. 55, 123507.

Sh, A Akimzhanova, Sakabekov (2019) Macroscopic boundary conditions on solid surface in rarefied gas flow for one-dimensional nonlinear nonstationary twelve moment Boltzmann system of equations. 59(10), 1710-1719.

S Pokhozhaev (1979) On an approach to nonlinear equation. 247, 1327-1331.

Luc Tartar (1979) The Compensated Compactness Method Applied to Systems of Conservation Laws. IV, 263-285.

Mixed Value Problem for a One-Dimensional Nonlinear Nonstationary Twelve moment BoltzmannS System Equations with the Maxwell-Auzhan Boundary Conditions

Published

2020-08-22

How to Cite

Mixed Value Problem for a One-Dimensional Nonlinear Nonstationary Twelve moment BoltzmannS System Equations with the Maxwell-Auzhan Boundary Conditions. (2020). Global Journal of Science Frontier Research, 20(F5), 37-47. https://www.journalofscience.org/index.php/GJSFR/article/view/2754