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Matematicheskie Zametki, 2009, Volume 85, Issue 1, Pages 36–53
DOI: https://doi.org/10.4213/mzm6584 (Mi mzm6584) 		 
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
Full-text PDF (558 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm6584
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.
Received: 26.11.2007
Revised: 17.03.2008
English version:
Mathematical Notes, 2009, Volume 85, Issue 1, Pages 34–50
DOI: https://doi.org/10.1134/S0001434609010040
Bibliographic databases:
UDC: 517.956.35
Language: Russian
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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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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