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1998, Volume 222  

| General information | Contents | Forward links |


Asymptotic methods of investigation of periodic solutions of nonlinear hyperbolic equations


Authors: A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov

ISBN: 5-02-002458-9

Abstract: The work deals with the asymptotic theory of time periodic solutions of hyperbolic type partial differential equations which simulate oscillation processes in self-excited oscillators with distributed parameters. Peculiarities of the dynamics of the equations in question, including gradient catastrophes, are established and the part played by resonance as a source of relaxation oscillation is revealed. The bufferness phenomenon observed in physical systems is theoretically justified.
The work is intended for researchers, higher school teachers, post-graduates who deal with differential equations and their applications, and for specialists who are interested in mathematical, physical and engeneering problems of the oscillation theory.


Citation: A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov, Asymptotic methods of investigation of periodic solutions of nonlinear hyperbolic equations, Tr. Mat. Inst. Steklova, 222, Nauka, MAIK Nauka, M., 1998, 192 pp.

Citation in format AMSBIB:
\Bibitem{1}
\by A.~Yu.~Kolesov, E.~F.~Mishchenko, N.~Kh.~Rozov
\book Asymptotic methods of investigation of periodic solutions of nonlinear hyperbolic equations
\serial Tr. Mat. Inst. Steklova
\yr 1998
\vol 222
\publ Nauka, MAIK Nauka
\publaddr M.
\totalpages 192
\mathnet{http://mi.mathnet.ru/book235}


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    Additional information

    The work deals with the asymptotic theory of time periodic solutions of hyperbolic type partial differential equations which simulate oscillation processes in self-excited oscillators with distributed parameters. Peculiarities of the dynamics of the equations in question, including gradient catastrophes, are established and the part played by resonance as a source of relaxation oscillation is revealed. The bufferness phenomenon observed in physical systems is theoretically justified.

    The work is intended for researchers, higher school teachers, post-graduates who deal with differential equations and their applications, and for specialists who are interested in mathematical, physical and engeneering problems of the oscillation theory.


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