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Mat. Zametki, 2009, Volume 85, Issue 1, Pages 36–53 (Mi mz6584)  

This article is cited in 3 scientific papers (total in 3 papers)

Periodic Solutions of a Quasilinear Wave Equation

V. A. Kondrat'eva, I. A. Rudakovb

a M. V. Lomonosov Moscow State University
b I. G. Petrovsky Bryansk State University

Abstract: We study the properties of wave operators satisfying the periodicity condition with respect to time and homogeneous boundary conditions of the third kind and of Dirichlet type. We prove the existence of a nontrivial periodic (in time) $\sin$-Gordon solution with homogeneous boundary conditions of the third kind and of Dirichlet type. We obtain theorems on the existence of periodic solutions of a quasilinear wave equation with variable (in $x$) coefficients and a boundary condition of the third kind.

Keywords: quasilinear wave equation, $\sin$-Gordon solution, boundary condition of the third kind, Dirichlet boundary condition, Sturm–Liouville problem, Sobolev space

DOI: https://doi.org/10.4213/mzm6584

Full text: PDF file (558 kB)
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English version:
Mathematical Notes, 2009, 85:1, 34–50

Bibliographic databases:

UDC: 517.956.35
Received: 26.11.2007
Revised: 17.03.2008

Citation: V. A. Kondrat'ev, I. A. Rudakov, “Periodic Solutions of a Quasilinear Wave Equation”, Mat. Zametki, 85:1 (2009), 36–53; Math. Notes, 85:1 (2009), 34–50

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm6584
  • http://mi.mathnet.ru/eng/mz/v85/i1/p36

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    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. Kharibegashvili S.S., Dzhokhadze O.M., “Time-Periodic Problem For a Weakly Nonlinear Telegraph Equation With Directional Derivative in the Boundary Condition”, Differ. Equ., 51:10 (2015), 1369–1386  crossref  mathscinet  zmath  isi  scopus
    2. S. S. Kharibegashvili, O. M. Dzhokhadze, “On solvability of a periodic problem for a nonlinear telegraph equation”, Siberian Math. J., 57:4 (2016), 735–743  mathnet  crossref  crossref  isi  elib  elib
    3. I. A. Rudakov, “Periodic Solutions of the Quasilinear Equation of Forced Vibrations of an Inhomogeneous String”, Math. Notes, 101:1 (2017), 137–148  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математические заметки Mathematical Notes
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