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

Pražák, Dalibor

doi:10.2478/BF02475219

Artykuł - szczegóły

Czasopismo

Open Mathematics

2003 | 1 | 3 | 411-417

Tytuł artykułu

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

Autorzy

Dalibor Pražák

Treść / Zawartość

Pełne teksty:

http://www.degruyter.com/view/j/math.2003.1.issue-3/BF02475219/bf02475219.pdf [zdalny]

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.

Słowa kluczowe

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

Wydawca

De Gruyter Open

Czasopismo

Open Mathematics

Rocznik

2003

Tom

Numer

Strony

411-417

Opis fizyczny

Daty

wydano

2003-09-01

online

2003-09-01

Twórcy

autor

Dalibor Pražák

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

DOI

10.2478/BF02475219

Identyfikator YADDA

bwmeta1.element.doi-10_2478_BF02475219