RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb., 2000, Volume 191, Number 8, Pages 45–68 (Mi msb498)  

This article is cited in 4 scientific papers (total in 4 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

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.

DOI: https://doi.org/10.4213/sm498

Full text: PDF file (305 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2000, 191:8, 1147–1169

Bibliographic databases:

UDC: 517.926
MSC: 35B10, 35B35, 35B40
Received: 08.12.1999

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
\Bibitem{KolRoz00}
\by A.~Yu.~Kolesov, N.~Kh.~Rozov
\paper Parametric excitation of high-mode oscillations for a~non-linear telegraph equation
\jour Mat. Sb.
\yr 2000
\vol 191
\issue 8
\pages 45--68
\mathnet{http://mi.mathnet.ru/msb498}
\crossref{https://doi.org/10.4213/sm498}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1786416}
\zmath{https://zbmath.org/?q=an:0980.35019}
\transl
\jour Sb. Math.
\yr 2000
\vol 191
\issue 8
\pages 1147--1169
\crossref{https://doi.org/10.1070/sm2000v191n08ABEH000498}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000165473200009}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0034354985}


Linking options:
  • http://mi.mathnet.ru/eng/msb498
  • https://doi.org/10.4213/sm498
  • http://mi.mathnet.ru/eng/msb/v191/i8/p45

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Yu. Kolesov, N. Kh. Rozov, “Optical Buffering and Mechanisms for Its Occurrence”, Theoret. and Math. Phys., 140:1 (2004), 905–917  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. E. P. Belan, “O dinamike beguschikh voln v parabolicheskom uravnenii s preobrazovaniem sdviga prostranstvennoi peremennoi”, Zhurn. matem. fiz., anal., geom., 1:1 (2005), 3–34  mathnet  mathscinet  zmath  elib
    3. Chen, SY, “Study on a new nonlinear parametric excitation equation: Stability and bifurcation”, Journal of Sound and Vibration, 318:4–5 (2008), 1109  crossref  isi  elib  scopus  scopus  scopus
    4. Kmit I., Recke L., “Solution Regularity and Smooth Dependence For Abstract Equations and Applications To Hyperbolic PDEs”, J. Differ. Equ., 259:11 (2015), 6287–6337  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:324
    Full text:89
    References:34
    First page:3

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019