Geodesic
On the existence of periodic solutions of an hyperbolic equation in a thin domain
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 8 (1997) no. 3, pp. 189-195.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

For a nonlinear hyperbolic equation defined in a thin domain we prove the existence of a periodic solution with respect to time both in the non-autonomous and autonomous cases. The methods employed are a combination of those developed by J. K. Hale and G. Raugel and the theory of the topological degree.
Si prova l'esistenza di soluzioni periodiche di un'equazione iperbolica smorzata definita in un dominio sottile sia nel caso autonomo che in quello non autonomo. I metodi impiegati sono una combinazione di quelli sviluppati da J. K. Hale e G. Raugel e la teoria del grado topologico. 
@article{RLIN_1997_9_8_3_a2,
     author = {Johnson, Russell and Kamenskii, Mikhail and Nistri, Paolo},
     title = {On the existence of periodic solutions of an hyperbolic equation in a thin domain},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {189--195},
     publisher = {mathdoc},
     volume = {Ser. 9, 8},
     number = {3},
     year = {1997},
     zbl = {0910.35008},
     mrnumber = {1383978},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1997_9_8_3_a2/}
}
TY  - JOUR
AU  - Johnson, Russell
AU  - Kamenskii, Mikhail
AU  - Nistri, Paolo
TI  - On the existence of periodic solutions of an hyperbolic equation in a thin domain
JO  - Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
PY  - 1997
SP  - 189
EP  - 195
VL  - 8
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RLIN_1997_9_8_3_a2/
LA  - en
ID  - RLIN_1997_9_8_3_a2
ER  - 
%0 Journal Article
%A Johnson, Russell
%A Kamenskii, Mikhail
%A Nistri, Paolo
%T On the existence of periodic solutions of an hyperbolic equation in a thin domain
%J Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
%D 1997
%P 189-195
%V 8
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RLIN_1997_9_8_3_a2/
%G en
%F RLIN_1997_9_8_3_a2
Johnson, Russell; Kamenskii, Mikhail; Nistri, Paolo. On the existence of periodic solutions of an hyperbolic equation in a thin domain. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 8 (1997) no. 3, pp. 189-195. http://geodesic.mathdoc.fr/item/RLIN_1997_9_8_3_a2/

[1] I. Ciuperca, Lower semicontinuity of attractors for a reaction-diffusion equation on thin domains with varying order of thinness. Preprint, Université de Paris-Sud, 1996. | DOI | MR

[2] I. Ciuperca, Reaction-diffusion equations on thin domains with varying order of thinness. Jour. Diff. Eqns., 126, 1996, 244-291. | DOI | MR | Zbl

[3] I. N. Gourova - M. I. Kamenskii, On the method of semidiscretization in periodic solutions problems for quasilinear autonomous parabolic equations. Differential Equations, 32, 1996, 101-106 (in Russian). | MR | Zbl

[4] J. Hale - G. Raugel, A damped hyperbolic equation on thin domains. Trans. Am. Math. Soc., 329, 1992, 185-219. | DOI | MR | Zbl

[5] J. Hale - G. Raugel, Reaction-diffusion equations in thin domains. Jour. Math. Pures et Appl., 71, 1992, 33-95. | MR | Zbl

[6] J. Hale - G. Raugel, Limits of semigroups depending on parameters. Resenhas IME-USP, 1, 1993, 1-45. | MR | Zbl

[7] R. Johnson - M. I. Kamenskii - P. Nistri, Existence of periodic solutions for an autonomous damped wave equation in a thin domain. Submitted. | Zbl

[8] R. Johnson - M. I. Kamenskii - P. Nistri, On periodic solutions of a damped wave equation in a thin domain using degree theoretic methods. Jour. Diff. Eqns., to appear. | DOI | MR | Zbl

[9] M. Krasnoselskii - P. Zabreiko - E. Pustyl'Nik - P. Sobolevski, Integral Operators in Spaces of Summable Functions. Noordhooff International Publishing, Leyden 1976. | MR | Zbl

[10] S. Krein, Linear Differential Equations in Banach Spaces. Nauka, Moscow 1967. | MR

[11] G. Raugel, Dynamics of partial differential equations in thin domains. Lecture Notes in Mathematics, Springer-Verlag, Berlin 1995, 1609, 208-315. | DOI | MR | Zbl