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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 172, Number 3, Pages 497–504
DOI: https://doi.org/10.4213/tmf6965 (Mi tmf6965) 		 
This article is cited in 22 scientific papers (total in 22 papers)

Qualitative difference between solutions for a model of the Boltzmann equation in the linear and nonlinear cases

A. Kh. Khachatryana, Kh. A. Khachatryanb

a Armenian State Agrarian University, Yerevan, Armenia
b Institute of Mathematics, Armenian National Academy of Sciences, Yerevan, Armenia
Full-text PDF (364 kB) Citations (22)
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DOI: https://doi.org/10.4213/tmf6965
Abstract: 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.
Received: 27.01.2012
English version:
Theoretical and Mathematical Physics, 2012, Volume 172, Issue 3, Pages 1315–1320
DOI: https://doi.org/10.1007/s11232-012-0116-4
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. Kh. Khachatryan, Kh. A. Khachatryan, “Qualitative difference between solutions for a model of the Boltzmann equation in the linear and nonlinear cases”, TMF, 172:3 (2012), 497–504; Theoret. and Math. Phys., 172:3 (2012), 1315–1320
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v172/i3/p497
    • This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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