| Title:
|
Dynamic von Kármán equations involving nonlinear damping: Time-periodic solutions (English) |
| Author:
|
Feireisl, Eduard |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
34 |
| Issue:
|
1 |
| Year:
|
1989 |
| Pages:
|
46-56 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
nonlinear damping |
| Keyword:
|
damped transversal vibrations |
| Keyword:
|
dynamic von Kármán equations |
| Keyword:
|
Faedo-Galerkin method |
| Keyword:
|
monotone operators on Orlicz spaces |
| Keyword:
|
time-periodic solution |
| MSC:
|
35B10 |
| MSC:
|
35J65 |
| MSC:
|
35Q20 |
| MSC:
|
35Q99 |
| MSC:
|
73K12 |
| MSC:
|
74H45 |
| MSC:
|
74K20 |
| idZBL:
|
Zbl 0676.73026 |
| idMR:
|
MR0982342 |
| DOI:
|
10.21136/AM.1989.104333 |
| . |
| Date available:
|
2008-05-20T18:35:56Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104333 |
| . |
| Reference:
|
[1] H. Gajewski K. Gröger K. Zacharias: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen.Akademie-Verlag Berlin 1974. MR 0636412 |
| Reference:
|
[2] A. Haraux: Dissipativity in the sense of Levinson for a class of second-order nonlinear evolution equations.Nonlinear Anal. 6 (1982), pp. 1207-1220. Zbl 0505.35012, MR 0683841, 10.1016/0362-546X(82)90031-1 |
| Reference:
|
[3] A. Kufner O. John S. Fučík: Function spaces.Academia Praha 1977. MR 0482102 |
| Reference:
|
[4] J. L. Lions: Quelques méthodes de résolution des problèmes aux limites non linéaires.Dunod, Gauthier-Villars, Paris 1969. Zbl 0189.40603, MR 0259693 |
| Reference:
|
[5] J. L. Lions, E. Magenes: Problèmes aux limites non homogènes et applications 1.Dunod, Paris 1968. |
| Reference:
|
[6] N. F. Morozov: Selected two-dimensional problems of the elasticity theory.(Russian.) Leningrad 1978. MR 0547112 |
| Reference:
|
[7] M. Nakao: Periodic solution and decay for some nonlinear wave equations with sublinear dissipative terms.Nonlinear Anal. 10 (1986), pp. 587 - 602. Zbl 0601.35075, MR 0844988, 10.1016/0362-546X(86)90144-6 |
| Reference:
|
[8] G. Prodi: Soluzioni periodiche di equazioni a derivative parziali di tipo iperbolico non lineari.Ann. Mat. Рurа Appl. 42 (1956), pp. 25 - 49. MR 0089985, 10.1007/BF02411872 |
| Reference:
|
[9] G. Prouse: Soluzioni periodiche dell'equazione deile onde non omogenea con termine dissipativo quadratico.Ricerche Mat. 13 (1964), pp. 261 - 280. MR 0194753 |
| Reference:
|
[10] P. H. Rabinowitz: Free vibrations for a semi-linear wave equation.Comm. Pure Appl. Math. 31 (1978), pp. 31-68. MR 0470378, 10.1002/cpa.3160310103 |
| Reference:
|
[11] A. Stahel: A remark on the equation of a vibrating plate.Proc. Royal Soc. Edinburgh 106 A (1987), pp. 307-314. Zbl 0625.73064, MR 0906214 |
| Reference:
|
[12] O. Vejvoda, al.: Partial differential equations: Time-periodic solutions.Martinus Nijhoff, The Hague 1982. Zbl 0501.35001 |
| Reference:
|
[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. MR 0618332 |
| . |
