Geodesic
Qualitative difference between solutions for a~model of the~Boltzmann equation in the~linear and nonlinear cases
Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 3, pp. 497-504

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We consider the Boltzmann equation in the framework of a nonlinear model for problems of the gas flow in a half-space (the Kramers problem). We prove the existence of a positive bounded solution and find the limit of this solution at infinity. We show that taking the nonlinear dependence of the collision integral on the distribution function into account leads to an asymptotically new solution of the initial equation. To illustrate the result, we present examples of functions describing the nonlinearity of the collision integral.
Keywords: Boltzmann equation, nonlinearity, mean mass velocity, bounded solution, monotonicity. 
@article{TMF_2012_172_3_a11,
     author = {A. Kh. Khachatryan and Kh. A. Khachatryan},
     title = {Qualitative difference between solutions for a~model of {the~Boltzmann} equation in the~linear and nonlinear cases},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {497--504},
     publisher = {mathdoc},
     volume = {172},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_172_3_a11/}
}
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A. Kh. Khachatryan; Kh. A. Khachatryan. Qualitative difference between solutions for a~model of the~Boltzmann equation in the~linear and nonlinear cases. Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 3, pp. 497-504. http://geodesic.mathdoc.fr/item/TMF_2012_172_3_a11/