Geodesic
Dynamic von Kármán equations involving nonlinear damping: Time-periodic solutions
Applications of Mathematics, Tome 34 (1989) no. 1, pp. 46-56
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/AM.1989.104333
Classification : 35B10, 35J65, 35Q20, 35Q99, 73K12, 74H45, 74K20
Keywords: nonlinear damping; damped transversal vibrations; dynamic von Kármán equations; Faedo-Galerkin method; monotone operators on Orlicz spaces; time-periodic solution 
@article{10_21136_AM_1989_104333,
     author = {Feireisl, Eduard},
     title = {Dynamic von {K\'arm\'an} equations involving nonlinear damping: {Time-periodic} solutions},
     journal = {Applications of Mathematics},
     pages = {46--56},
     year = {1989},
     volume = {34},
     number = {1},
     doi = {10.21136/AM.1989.104333},
     mrnumber = {0982342},
     zbl = {0676.73026},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1989.104333/}
}
TY  - JOUR
AU  - Feireisl, Eduard
TI  - Dynamic von Kármán equations involving nonlinear damping: Time-periodic solutions
JO  - Applications of Mathematics
PY  - 1989
SP  - 46
EP  - 56
VL  - 34
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1989.104333/
DO  - 10.21136/AM.1989.104333
LA  - en
ID  - 10_21136_AM_1989_104333
ER  - 
%0 Journal Article
%A Feireisl, Eduard
%T Dynamic von Kármán equations involving nonlinear damping: Time-periodic solutions
%J Applications of Mathematics
%D 1989
%P 46-56
%V 34
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1989.104333/
%R 10.21136/AM.1989.104333
%G en
%F 10_21136_AM_1989_104333
Feireisl, Eduard. Dynamic von Kármán equations involving nonlinear damping: Time-periodic solutions. Applications of Mathematics, Tome 34 (1989) no. 1, pp. 46-56. doi: 10.21136/AM.1989.104333

[1] H. Gajewski K. Gröger K. Zacharias: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Akademie-Verlag Berlin 1974. | MR

[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. | DOI | MR | Zbl

[3] A. Kufner O. John S. Fučík: Function spaces. Academia Praha 1977. | MR

[4] J. L. Lions: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Gauthier-Villars, Paris 1969. | MR | Zbl

[5] J. L. Lions, E. Magenes: Problèmes aux limites non homogènes et applications 1. Dunod, Paris 1968.

[6] N. F. Morozov: Selected two-dimensional problems of the elasticity theory. (Russian.) Leningrad 1978. | MR

[7] M. Nakao: Periodic solution and decay for some nonlinear wave equations with sublinear dissipative terms. Nonlinear Anal. 10 (1986), pp. 587 - 602. | DOI | MR | Zbl

[8] G. Prodi: Soluzioni periodiche di equazioni a derivative parziali di tipo iperbolico non lineari. Ann. Mat. Рurа Appl. 42 (1956), pp. 25 - 49. | DOI | MR

[9] G. Prouse: Soluzioni periodiche dell'equazione deile onde non omogenea con termine dissipativo quadratico. Ricerche Mat. 13 (1964), pp. 261 - 280. | MR

[10] P. H. Rabinowitz: Free vibrations for a semi-linear wave equation. Comm. Pure Appl. Math. 31 (1978), pp. 31-68. | DOI | MR

[11] A. Stahel: A remark on the equation of a vibrating plate. Proc. Royal Soc. Edinburgh 106 A (1987), pp. 307-314. | MR | Zbl

[12] O. Vejvoda, al.: Partial differential equations: Time-periodic solutions. Martinus Nijhoff, The Hague 1982. | Zbl

[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

Cité par Sources :