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Title: Small time-periodic solutions to a nonlinear equation of a vibrating string (English)
Author: Feireisl, Eduard
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 32
Issue: 6
Year: 1987
Pages: 480-490
Summary lang: English
Summary lang: Russian
Summary lang: Czech
Category: math
Summary: In this paper, the system consisting of two nonlinear equations is studied. The former is hyperbolic with a dissipative term and the latter is elliptic. In a special case, the system reduces to the approximate model for the damped transversal vibrations of a string proposed by G. F. Carrier and R. Narasimha. Taking advantage of accelerated convergence methods, the existence of at least one time-periodic solution is stated on condition that the right-hand side of the system is sufficiently small. (English)
Keyword: nonlinear string equation
Keyword: accelerated convergence
Keyword: existence
Keyword: periodic
Keyword: Dirichlet boundary conditions
Keyword: vibrations
Keyword: damped extensive string
Keyword: time-periodic solution
MSC: 35B10
MSC: 35L70
MSC: 58C15
MSC: 73K03
idZBL: Zbl 0653.35063
idMR: MR0916063
DOI: 10.21136/AM.1987.104278
Date available: 2008-05-20T18:33:33Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] R. W. Dickey: Infinite systems of nonlinear oscillation equations with Linear Damping.Siam J. Appl. Math. 19 (1970), pp. 208-214. Zbl 0233.34014, MR 0265654, 10.1137/0119019
Reference: [2] S. Klainerman: Global existence for nonlinear wave equations.Comm. Pure Appl. Math. 33 (1980), pp. 43--101. Zbl 0405.35056, MR 0544044, 10.1002/cpa.3160330104
Reference: [3] P. Krejčí: Hard Implicit Function Theorem and Small periodic solutions to partial differential equations.Comment. Math. Univ. Carolinae 25 (1984), pp. 519-536. MR 0775567
Reference: [4] J. Moser: A rapidly-convergent iteration method and nonlinear differential equations.Ann. Scuola Norm. Sup. Pisa 20-3 (1966), pp. 265-315, 499-535.
Reference: [5] O. Vejvoda, et al.: Partial differential equations: Time-periodic Solutions.Martinus Nijhoff Publ., 1982. Zbl 0501.35001


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