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

Dalibor Pražák

Open Mathematics (2003)

  • Volume: 1, Issue: 3, page 411-417
  • ISSN: 2391-5455

Abstract

top
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.

How to cite

top

Dalibor Pražák. "A necessary and sufficient condition for the existence of an exponential attractor." Open Mathematics 1.3 (2003): 411-417. <http://eudml.org/doc/268751>.

@article{DaliborPražák2003,
abstract = {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.},
author = {Dalibor Pražák},
journal = {Open Mathematics},
keywords = {37L25; 37L30; 35L70},
language = {eng},
number = {3},
pages = {411-417},
title = {A necessary and sufficient condition for the existence of an exponential attractor},
url = {http://eudml.org/doc/268751},
volume = {1},
year = {2003},
}

TY - JOUR
AU - Dalibor Pražák
TI - A necessary and sufficient condition for the existence of an exponential attractor
JO - Open Mathematics
PY - 2003
VL - 1
IS - 3
SP - 411
EP - 417
AB - 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.
LA - eng
KW - 37L25; 37L30; 35L70
UR - http://eudml.org/doc/268751
ER -

References

top
  1. [1] [EFNT] A. Eden, C. Foias, B. Nicolaenko, R. Temam: Exponential attractors for dissipative evolution equations, Wiley & Masson, Chichester, Paris, 1994. 
  2. [2] [EM] M. Efendiev and A. Miranville: On the dimension of the global attractor for dissipative reaction-diffusion systems, Preprint. 
  3. [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 Zbl1151.35315
  4. [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 Zbl0819.35097
  5. [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. [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 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.