Dynamic von Kármán equations involving nonlinear damping: Time-periodic solutions

Eduard Feireisl

Aplikace matematiky (1989)

  • Volume: 34, Issue: 1, page 46-56
  • ISSN: 0862-7940

Abstract

top
In the paper, time-periodic solutions to dynamic von Kármán equations are investigated. Assuming that there is a damping term in the equations we are able to show the existence of at least one solution to the problem. The Faedo-Galerkin method is used together with some basic ideas concerning monotone operators on Orlicz spaces.

How to cite

top

Feireisl, Eduard. "Dynamic von Kármán equations involving nonlinear damping: Time-periodic solutions." Aplikace matematiky 34.1 (1989): 46-56. <http://eudml.org/doc/15563>.

@article{Feireisl1989,
abstract = {In the paper, time-periodic solutions to dynamic von Kármán equations are investigated. Assuming that there is a damping term in the equations we are able to show the existence of at least one solution to the problem. The Faedo-Galerkin method is used together with some basic ideas concerning monotone operators on Orlicz spaces.},
author = {Feireisl, Eduard},
journal = {Aplikace matematiky},
keywords = {nonlinear damping; damped transversal vibrations; dynamic von Kármán equations; Faedo-Galerkin method; monotone operators on Orlicz spaces; time-periodic solution; nonlinear damping; damped transversal vibrations; dynamic von Kármán equations; Faedo-Galerkin method; monotone operators on Orlicz spaces},
language = {eng},
number = {1},
pages = {46-56},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Dynamic von Kármán equations involving nonlinear damping: Time-periodic solutions},
url = {http://eudml.org/doc/15563},
volume = {34},
year = {1989},
}

TY - JOUR
AU - Feireisl, Eduard
TI - Dynamic von Kármán equations involving nonlinear damping: Time-periodic solutions
JO - Aplikace matematiky
PY - 1989
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 34
IS - 1
SP - 46
EP - 56
AB - In the paper, time-periodic solutions to dynamic von Kármán equations are investigated. Assuming that there is a damping term in the equations we are able to show the existence of at least one solution to the problem. The Faedo-Galerkin method is used together with some basic ideas concerning monotone operators on Orlicz spaces.
LA - eng
KW - nonlinear damping; damped transversal vibrations; dynamic von Kármán equations; Faedo-Galerkin method; monotone operators on Orlicz spaces; time-periodic solution; nonlinear damping; damped transversal vibrations; dynamic von Kármán equations; Faedo-Galerkin method; monotone operators on Orlicz spaces
UR - http://eudml.org/doc/15563
ER -

References

top
  1. H. Gajewski K. Gröger K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag Berlin 1974. (1974) MR0636412
  2. A. Haraux, 10.1016/0362-546X(82)90031-1, Nonlinear Anal. 6 (1982), pp. 1207-1220. (1982) Zbl0505.35012MR0683841DOI10.1016/0362-546X(82)90031-1
  3. A. Kufner O. John S. Fučík, Function spaces, Academia Praha 1977. (1977) MR0482102
  4. J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Gauthier-Villars, Paris 1969. (1969) Zbl0189.40603MR0259693
  5. J. L. Lions, E. Magenes, Problèmes aux limites non homogènes et applications 1, Dunod, Paris 1968. (1968) 
  6. N. F. Morozov, Selected two-dimensional problems of the elasticity theory, (Russian.) Leningrad 1978. (1978) MR0547112
  7. M. Nakao, 10.1016/0362-546X(86)90144-6, Nonlinear Anal. 10 (1986), pp. 587 - 602. (1986) Zbl0601.35075MR0844988DOI10.1016/0362-546X(86)90144-6
  8. G. Prodi, 10.1007/BF02411872, Ann. Mat. Рurа Appl. 42 (1956), pp. 25 - 49. (1956) MR0089985DOI10.1007/BF02411872
  9. G. Prouse, Soluzioni periodiche dell'equazione deile onde non omogenea con termine dissipativo quadratico, Ricerche Mat. 13 (1964), pp. 261 - 280. (1964) MR0194753
  10. P. H. Rabinowitz, 10.1002/cpa.3160310103, Comm. Pure Appl. Math. 31 (1978), pp. 31-68. (1978) MR0470378DOI10.1002/cpa.3160310103
  11. A. Stahel, A remark on the equation of a vibrating plate, Proc. Royal Soc. Edinburgh 106 A (1987), pp. 307-314. (1987) Zbl0625.73064MR0906214
  12. O. Vejvoda, al., Partial differential equations: Time-periodic solutions, Martinus Nijhoff, The Hague 1982. (1982) Zbl0501.35001
  13. W. von Wahl, On nonlinear evolution equations in a Banach space and nonlinear vibrations of the clamped plate, Bayreuther Mathematische Schriften, 7 (1981), pp. 1 - 93. (1981) MR0618332

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.