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On One Nonlinear Boundary-Value Problem in Kinetic Theory of Gases
A. Kh. Khachatryana, Kh. A. Khachatryanb, T. H. Sardaryanb a Armenian National Agrarian University, 74 Teryan St., Yerevan, 0009, Armenia
b Institute of Mathematics of National Academy of Sciences of Armenia, 24/5 Baghramyan Ave., Yerevan 0019, Armenia
Abstract:
In the paper, the solvability of one nonlinear boundary-value problem arising in kinetic theory of gases is studied. We prove the existence of global solvability of a boundary-value problem in the Sobolev space $W_{\infty}^1(\mathbb{R}^+).$ The limit of the solution is found by using some a'priori estimations. For the case of power nonlinearity, the uniqueness of the solution in a certain class of functions is proved. Some examples illustrating the obtained results are given.
Key words and phrases:
boundary-value problem, monotony, nonlinear integral equation, iteration, limit of solution.
Received: 09.09.2013 Revised: 05.02.2014
Citation:
A. Kh. Khachatryan, Kh. A. Khachatryan, T. H. Sardaryan, “On One Nonlinear Boundary-Value Problem in Kinetic Theory of Gases”, Zh. Mat. Fiz. Anal. Geom., 10:3 (2014), 320–327
Linking options:
https://www.mathnet.ru/eng/jmag597 https://www.mathnet.ru/eng/jmag/v10/i3/p320
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Abstract page: | 443 | Full-text PDF : | 139 | References: | 48 |
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