Abstract
The statement of nonlinear boundary conditions for the Boltzmann kinetic equation is examined. On this basis, the possibility is discussed that relaxation- or preturbulent-type oscillations that are asymptotically periodic can form in gases.
Similar content being viewed by others
References
E. G. Cohen and W. Thirring (eds.), “The Boltzmann equation. Theory and applications,” in:Proc. of the Int. Symposium, Wien, 1972, Springer, Wien-New York (1973).
A. N. Sharkovsky, Yu. L. Maistrenko, and E. Yu. Romanenko,Difference Equations and Their Applications [in Russian], Naukova Dumka, Kiev (1986).
I. B. Krasniuk,Inzh.-Fiz. Zh.,67, Nos. 1,2, 324 (1994).
I. B. Krasniuk and B. L. Revzin,Inzh.-Fiz. Zh.,67, Nos. 3,4, 167 (1994).
I. B. Krasniuk,Inzh.-Fiz. Zh.,67, Nos. 1,2, 162 (1994).
I. B. Krasniuk and T. T. Riskiev,Opt. Spektrosk.,75, 517 (1993).
I. B. Krasniuk, T. T. Riskiev, and B. L. Revzin,Uzb. Fiz. Zh.,4, 5 (1993).
I. B. Krasniuk, T. T. Riskiev, and A. A. Streltsov,Uzb. Fiz. Zh.,1, 50 (1994).
I. B. Krasniuk, “Systems with concurrent relaxation-type interaction oscillations,” in:Proc. Int. Conf. on Bifurcations and Chaos, Crimea (1994).
I. B. Krasniuk, “On one generalization of the nonlinear hyperbolic boundary-value problem on a surface,” in:Differential-Difference Equations and Problems of Mathematical Physics [in Russian], Institute of Mathematics, Kiev (1984), p. 38.
M. Kac,Some Stochastic Problems in Physics and Mathematics (Coll. Lectures in Pure and Applied Science, No. 2), Magnolia Petroleum Co. (1956).
V. P. Maslov, V. G. Danilov, and K. A. Volosov,Mathematical Modeling of Heat and Mass Transform Processes, Kluwer, Dordrecht-Boston-London (1995).
N. N. Bogoliubov and Yu. A. Mitropolski,Les Méthodes Asymptotiques en Théorie des Oscillations Nonlinéaires, Granthier-Villars, Paris (1962).
V. P. Maslov,Complex Method for Nonlinear Equations, Vol. 1, Birhäuser, Basel-Boston-Berlin (1994).
G. Wentzel,Quantum Theory of Fields, Interscience Publ., New York-London (1949).
V. K. Godunov and A. A. Sultagazin,Usp. Mat. Nauk,26, No. 3, 3 (1971).
V. V. Vedenyapin, “On a theorem for the existence of a global solution to the Cauchy problem for nonlinear hyperbolic systems of partial differential equations (with applications to discrete models of the Boltzmann equation),” Preprint IPM RAN No. 42 (1973).
I. B. Krasniuk,Dokl. Akad. Nauk Ukr. SSR, Ser. A,6, 20 (1989).
A. N. Sharkovsky, I. B. Krasniuk, and Yu. L. Maistrenko,Dokl. Akad. Nauk Ukr. SSR,12, 27 (1984).
Author information
Authors and Affiliations
Additional information
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 2, pp. 323–333, February, 1997.
Rights and permissions
About this article
Cite this article
Krasniuk, I.B. Nonlinear boundary-value problems for Boltzmann equations: Periodic solutions and their bifurcations. Theor Math Phys 110, 256–264 (1997). https://doi.org/10.1007/BF02630451
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02630451