A necessary and sufficient condition for the existence of an exponential attractor

• Autorzy: Dalibor Pražák
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

global attractor; exponential attractor; fractal dimension; wave equation; nonlinear damping; 37L25; 37L30; 35L70

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2003
• Tom: 1
• Numer: 3
• Strony: 411-417

Daty

wydano

2003-09-01

online

2003-09-01

Twórcy

autor

Dalibor Pražák

• Charles University, Prague

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

Identyfikatory

DOI

10.2478/BF02475219