Time-periodic solutions of a quasilinear beam equation via accelerated convergence methods
Feireisl, Eduard
Applications of Mathematics, Tome 33 (1988), p. 362-373 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1988-01-01
Classification:  35B10,  35L70,  35L75,  58C15,  65N35,  65Z05,  73K05,  74K10 
@article{104317,
     author = {Eduard Feireisl},
     title = {Time-periodic solutions of a quasilinear beam equation via accelerated convergence methods},
     journal = {Applications of Mathematics},
     volume = {33},
     year = {1988},
     pages = {362-373},
     zbl = {0665.65090},
     mrnumber = {0961314},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104317}
}

Feireisl, Eduard. Time-periodic solutions of a quasilinear beam equation via accelerated convergence methods. Applications of Mathematics, Tome 33 (1988) pp. 362-373. http://gdmltest.u-ga.fr/item/104317/

L. Hörmander On the Nash-Moser implicit function theorem, Annal. Acad. Sci. Fennicae, Ser. A, 10 (1985) pp. 255-259. (1985) | MR 0802486

S. Klainerman Global existence for nonlinear wave equations, Comm. Pure Appl. Math. 33 (1980), pp. 43-101. (1980) | Article | MR 0544044 | Zbl 0405.35056

P. Krejčí Hard implicit function theorem and small periodic solutions to partial differential equations, Comment. Math. Univ. Carolinae 25 (1984), pp. 519-536. (1984) | MR 0775567

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. (1977) | Article | MR 0470507 | Zbl 0371.35030

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) | Zbl 0174.47801

H. Petzeltová Application of Moser's method to a certain type of evolution equations, Czechoslovak Math. J. 33 (1983), pp. 427-434. (1983) | MR 0718925 | Zbl 0547.35081

H. Petzeltová M. Štědrý Time-periodic solutions of telegraph equations in n spatial variables, Časopis pěst. mat. 109 (1984), pp. 60-73. (1984) | MR 0741209

M. Štědrý Periodic solutions of nonlinear equations of a beam with damping, Czech. Thesis, Math. Inst. Czechoslovak Acad. Sci., Prague 1973. (1973)

O. Vejvoda; Al. Partial differential equations - time periodic solutions, Sijthoff Noordhoff 1981. (1981)