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Title: Time-periodic solutions of a quasilinear beam equation via accelerated convergence methods (English)
Author: Feireisl, Eduard
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 33
Issue: 5
Year: 1988
Pages: 362-373
Summary lang: English
Summary lang: Russian
Summary lang: Czech
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Category: math
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Summary: The author investigates time-periodic solutions of the quasilinear beam equation with the help of accelerated convergence methods. Using the Newton iteration scheme, the problem is approximated by a sequence of linear equations solved via the Galerkin method. The derivatiove loss inherent to this kind of problems is compensated by taking advantage of smoothing operators. (English)
Keyword: accelerated convergence methods
Keyword: smoothing operators
Keyword: time-periodic solutions
Keyword: quasilinear beam equation
Keyword: Newton method
Keyword: Galerkin method
MSC: 35B10
MSC: 35L70
MSC: 35L75
MSC: 58C15
MSC: 65N35
MSC: 65Z05
MSC: 73K05
MSC: 74K10
idZBL: Zbl 0665.65090
idMR: MR0961314
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Date available: 2008-05-20T18:35:15Z
Last updated: 2015-06-03
Stable URL: http://hdl.handle.net/10338.dmlcz/104317
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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] A. Matsumura: Global existence and asymptotics of the solutions of the second order quasilinear hyperbolic equations with the first order dissipation.Publ. Res. Inst. Math. Soc. 13 (1977), pp. 349-379. Zbl 0371.35030, MR 0470507, 10.2977/prims/1195189813
Reference: [5] J. Moser: A rapidly-convergent iteration method and non-linear differential equations.Ann. Scuola Norm. Sup. Pisa 20-3 (1966), pp. 265-315, 499-535. Zbl 0174.47801
Reference: [6] H. Petzeltová: Application of Moser's method to a certain type of evolution equations.Czechoslovak Math. J. 33 (1983), pp. 427-434. Zbl 0547.35081, MR 0718925
Reference: [7] H. Petzeltová M. Štědrý: Time-periodic solutions of telegraph equations in n spatial variables.Časopis pěst. mat. 109 (1984), pp. 60-73. MR 0741209
Reference: [8] M. Štědrý: Periodic solutions of nonlinear equations of a beam with damping.Czech. Thesis, Math. Inst. Czechoslovak Acad. Sci., Prague 1973.
Reference: [9] O. Vejvoda, al.: Partial differential equations - time periodic solutions.Sijthoff Noordhoff 1981.
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