Geodesic
Asymptotic Methods of Investigation of Periodic Solutions of Nonlinear Hyperbolic Equations
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Asymptotic methods of investigation of periodic solutions of nonlinear hyperbolic equations, Tome 222 (1998), pp. 3-191 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{TM_1998_222_a0,
     author = {A. Yu. Kolesov and E. F. Mishchenko and N. Kh. Rozov},
     title = {Asymptotic {Methods} of {Investigation} of {Periodic} {Solutions} of {Nonlinear} {Hyperbolic} {Equations}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {3--191},
     year = {1998},
     volume = {222},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_1998_222_a0/}
}
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A. Yu. Kolesov; E. F. Mishchenko; N. Kh. Rozov. Asymptotic Methods of Investigation of Periodic Solutions of Nonlinear Hyperbolic Equations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Asymptotic methods of investigation of periodic solutions of nonlinear hyperbolic equations, Tome 222 (1998), pp. 3-191. http://geodesic.mathdoc.fr/item/TM_1998_222_a0/