Geodesic
Some solvability problems for the~Boltzmann equation in the~framework of the~Shakhov model
Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 3, pp. 441-455

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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.
Keywords: nonlinearity, monotonicity, model equation, iteration, temperature jump, kinetic thickness. 
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     author = {A. Kh. Khachatryan and A. A. Khachatryan},
     title = {Some solvability problems for {the~Boltzmann} equation in the~framework of {the~Shakhov} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {441--455},
     publisher = {mathdoc},
     volume = {191},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_191_3_a5/}
}
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A. Kh. Khachatryan; A. A. Khachatryan. Some solvability problems for the~Boltzmann equation in the~framework of the~Shakhov model. Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 3, pp. 441-455. http://geodesic.mathdoc.fr/item/TMF_2017_191_3_a5/