Time-periodic solutions of a quasilinear beam equation via accelerated convergence methods

Eduard Feireisl

Aplikace matematiky (1988)

  • Volume: 33, Issue: 5, page 362-373
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Feireisl, Eduard. "Time-periodic solutions of a quasilinear beam equation via accelerated convergence methods." Aplikace matematiky 33.5 (1988): 362-373. <http://eudml.org/doc/15550>.

@article{Feireisl1988,
abstract = {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.},
author = {Feireisl, Eduard},
journal = {Aplikace matematiky},
keywords = {accelerated convergence methods; smoothing operators; time-periodic solutions; quasilinear beam equation; Newton method; Galerkin method; accelerated convergence methods; smoothing operators; time-periodic solutions; quasilinear beam equation; Newton method; Galerkin method},
language = {eng},
number = {5},
pages = {362-373},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Time-periodic solutions of a quasilinear beam equation via accelerated convergence methods},
url = {http://eudml.org/doc/15550},
volume = {33},
year = {1988},
}

TY - JOUR
AU - Feireisl, Eduard
TI - Time-periodic solutions of a quasilinear beam equation via accelerated convergence methods
JO - Aplikace matematiky
PY - 1988
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 33
IS - 5
SP - 362
EP - 373
AB - 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.
LA - eng
KW - accelerated convergence methods; smoothing operators; time-periodic solutions; quasilinear beam equation; Newton method; Galerkin method; accelerated convergence methods; smoothing operators; time-periodic solutions; quasilinear beam equation; Newton method; Galerkin method
UR - http://eudml.org/doc/15550
ER -

References

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  1. L. Hörmander, On the Nash-Moser implicit function theorem, Annal. Acad. Sci. Fennicae, Ser. A, 10 (1985) pp. 255-259. (1985) Zbl0591.58003MR0802486
  2. S. Klainerman, 10.1002/cpa.3160330104, Comm. Pure Appl. Math. 33 (1980), pp. 43-101. (1980) Zbl0405.35056MR0544044DOI10.1002/cpa.3160330104
  3. P. Krejčí, Hard implicit function theorem and small periodic solutions to partial differential equations, Comment. Math. Univ. Carolinae 25 (1984), pp. 519-536. (1984) Zbl0567.35007MR0775567
  4. A. Matsumura, 10.2977/prims/1195189813, Publ. Res. Inst. Math. Soc. 13 (1977), pp. 349-379. (1977) Zbl0371.35030MR0470507DOI10.2977/prims/1195189813
  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. (1966) Zbl0174.47801
  6. H. Petzeltová, Application of Moser's method to a certain type of evolution equations, Czechoslovak Math. J. 33 (1983), pp. 427-434. (1983) Zbl0547.35081MR0718925
  7. H. Petzeltová M. Štědrý, Time-periodic solutions of telegraph equations in n spatial variables, Časopis pěst. mat. 109 (1984), pp. 60-73. (1984) Zbl0544.35011MR0741209
  8. M. Štědrý, Periodic solutions of nonlinear equations of a beam with damping, Czech. Thesis, Math. Inst. Czechoslovak Acad. Sci., Prague 1973. (1973) 
  9. O. Vejvoda, al., Partial differential equations - time periodic solutions, Sijthoff Noordhoff 1981. (1981) 

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