Theoretical and Mathematical Physics

, Volume 191, Issue 3, pp 856–869 | Cite as

Some solvability problems for the Boltzmann equation in the framework of the Shakhov model

  • A. Kh. Khachatryan
  • A. A. Khachatryan


We consider the nonlinear Boltzmann equation in the framework of the Shakhov model for the classical problem of gas flow in a plane layer. The problem reduces to a system of nonlinear integral equations. The nonlinearity of the studied system can be partially simplified by passing to a new argument depending on the solution of the problem itself. We prove the existence theorem for a unique solution of the linear system and the existence theorem for a positive solution of the nonlinear Urysohn equation. We determine the temperature jumps on the lower and upper walls in the linear and nonlinear cases, and it turns out that the difference between them is rather small.


nonlinearity monotonicity model equation iteration temperature jump kinetic thickness 


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© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Faculty of Higher Mathematics and Theoretical MechanicsArmenian National Agrarian UniversityErevanArmenia

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