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

Open Mathematics (2003)

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

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topDalibor 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] [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 Zbl1151.35315
- [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] [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

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