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Sbornik: Mathematics, 2000, Volume 191, Issue 8, Pages 1147–1169
DOI: https://doi.org/10.1070/sm2000v191n08ABEH000498 (Mi sm498) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Parametric excitation of high-mode oscillations for a non-linear telegraph equation

A. Yu. Kolesova, N. Kh. Rozovb

a P. G. Demidov Yaroslavl State University
b M. V. Lomonosov Moscow State University
English version PDF (253 kB) Citations (5)
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DOI: https://doi.org/10.1070/sm2000v191n08ABEH000498
Abstract: The problem of parametric excitation of high-mode oscillations is solved for a non-linear telegraph equation with a parametric external excitation and small diffusion. The equation is considered on a finite (spatial) interval with Neumann boundary conditions. It is shown that under a proper choice of parameters of the external excitation this boundary-value problem can have arbitrarily many exponentially stable solutions that are periodic in time and rapidly oscillate with respect to the spatial variable.
Received: 08.12.1999
Russian version:
Matematicheskii Sbornik, 2000, Volume 191, Number 8, Pages 45–68
DOI: https://doi.org/10.4213/sm498
Bibliographic databases:
UDC: 517.926
MSC: 35B10, 35B35, 35B40
Language: English
Original paper language: Russian
Citation: A. Yu. Kolesov, N. Kh. Rozov, “Parametric excitation of high-mode oscillations for a non-linear telegraph equation”, Mat. Sb., 191:8 (2000), 45–68; Sb. Math., 191:8 (2000), 1147–1169
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    English version PDF:11
    References:65
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