Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We give a necessary and sufficient condition for the existence of an exponential attractor. The condition is formulated in the context of metric spaces. It also captures the quantitative properties of the attractor, i.e., the dimension and the rate of attraction. As an application, we show that the evolution operator for the wave equation with nonlinear damping has an exponential attractor.
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
411-417
Opis fizyczny
Daty
wydano
2003-09-01
online
2003-09-01
Twórcy
autor
- Charles University, Prague, prazak@karlin.mff.cuni.cz
Bibliografia
- [1] [EFNT] A. Eden, C. Foias, B. Nicolaenko, R. Temam: Exponential attractors for dissipative evolution equations, Wiley & Masson, Chichester, Paris, 1994.
- [2] [EM] M. Efendiev and A. Miranville: On the dimension of the global attractor for dissipative reaction-diffusion systems, Preprint.
- [3] [EMZ] M. Efendiev, A. Miranville, S. Zelik: “Exponential attractors for a nonlinear reaction-diffusion system in R 3”, Comptes-Rendus de l’Académie des Sciences, Vol. 330, (2000), pp. 713–718. http://dx.doi.org/10.1016/S0764-4442(00)00259-7
- [4] [F] E. Feireisl: “Global attractors for semilinear damped wave equations with supercritical exponent”, J. Differential Equations, Vol. 116, (1995), pp. 431–447. http://dx.doi.org/10.1006/jdeq.1995.1042
- [5] [MP] J. Málek and D. Pražák: “Large time behavior via the method of ℓ-trajectories”, J. Differential Equations, Vol. 181, (2002), pp. 243–279. http://dx.doi.org/10.1006/jdeq.2001.4087
- [6] [P] D. Pražák: “On finite fractal dimension of the global attractor for the wave equation with nonlinear damping”, J. Dynamics Differential Equations, Vol. 14, (2002), pp. 763–776. http://dx.doi.org/10.1023/A:1020756426088
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475219