Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems

Royal Society of Edinburgh - Proceedings A

Volumn 135, Issue 4, 2005, Pages 703-730

  Efendiev, M ^a   Zelik, S ^a   Miranville, A ^b  

^a UNIVERSITY OF STUTTGART   (Germany)

^b UNIVERSITÉ DE POITIERS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27644506450     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/s030821050000408x     Document Type: Article

References (27)

1. A. Babin and M. Vishik. Attractors of evolutionary equations (Moscow: Nauka, 1989).
2. (English transl. in Studies in Mathematics and Its Applications, vol. 25 (Amsterdam: North-Holland, 1992).)
3. D. Cheban, P. Kloeden and B. Schmalfuss. The relationship between pullback, forwards and global attractors of nonautonomous dynamical systems. Nonlin. Dynam. Syst. Theory 2 (2002), 9-28.
4. V. Chepyzhov and M. Vishik. Attractors of non-autonomous dynamical systems and their dimension. J. Math. Pures Appl. 73 (1994), 279-333.
5. V. Chepyzhov and M. Vishik. Non-autonomous evolutionary equations with translation-compact symbols and their attractors. C. R. Acad. Sci. Paris Sér. I 321 (1995), 153-158.
6. V. Chepyzhov and M. Vishik. Kolmogorov's ε-entropy for the attractor of reaction-diffusion equations. Mat. USSR Sb. 189 (1998), 81-110.
7. V. Chepyzhov and M. Vishik. Attractors for equations of mathematical physics (Providence, RI: American Mathematical Society, 2002).
8. H. Crauel and F. Flandoli. Attractors for random dynamical systems. Probab. Theory Relat. Fields 100 (1994), 365-393.
9. A. Eden, C. Foias, B. Nicolaenko and R. Temam. Exponential attractors for dissipative evolution equations. Research in Applied Mathematics, vol. 37 (Wiley, 1994).
10. M. Efendiev and S. Zelik. The regular attractor for the reaction-diffusion system with a nonlinearity rapidly oscillating in time and its averaging. Adv. Diff. Eqns 8 (2003), 673-732.
11. 3. C. R. Acad. Sci. Paris Sér. I 330 (2000), 713-718.
12. M. Efendiev, A. Miranville and S. Zelik. Infinite dimensional attractors for a non-autonomous reaction-diffusion system. Math. Nachr. 248/249 (2003), 72-96.
13. M. Efendiev, A. Miranville and S. Zelik. Exponential attractors for a singularly perturbed Cahn-Hilliard system. Math. Nachr. 272 (2004), 11-31.
14. P. Fabrie and A. Miranville. Exponential attractors for nonautonomous first-order evolution equations. Discrete Contin. Dynam. Syst. 4 (1998), 225-240.
15. P. Fabrie, C. Galusinski, A. Miranville and S. Zelik. Uniform exponential attractors for a singularly perturbed damped wave equation. Discrete Contin. Dynam. Syst. 10 (2004), 211-238.
16. J. Hale. Asymptotic behavior of dissipative systems. In Mathematical Surveys and Monographs, vol. 25 (Providence, RI: American Mathematical Society, 1987).
17. A. Haraux. Systèmes dynamiques dissipatifs (Paris: Masson, 1991).
18. P. Kloeden. Pullback attractors of nonautonomous semidynamical systems. Stock. Dyn. 3 (2003), 101-112.
19. O. Ladyzhenskaya. Attractors for semigroups of evolution equations (Cambridge University Press, 1991).
20. A. Miranville. Exponential attractors for non-autonomous evolution equations. Appl. Math. Lett. 11 (1998), 19-22.
21. A. Miranville. Exponential attractors for a class of evolution equations by a decomposition method. II. The nonautonomous case. C. R. Acad. Sci. Paris Sér. I 328 (1999), 907-912.
22. A. Miranville and S. Zelik. Robust exponential attractors for Cahn-Hilliard type equations with singular potentials. Math. Meth. Appl. Sci. 27 (2004), 545-582.
23. B. Schmalfuss. Attractors for the non-autonomous dynamical systems. In Proc. of EQUADIFF99 (ed. K. Gröger, B. Fiedler and J. Sprekels) (World Scientific, 2000).
24. R. Temam. Infinite-dimensional dynamical systems in mechanics and physics (Springer, 1988).
25. M. Vishik and A. Goritskij. Integral manifolds for nonautonomous equations. Rend. Acad. Naz. Scienze detta dei XL, Mem. Mat. Appl. 5 (1997), 109-146.
26. Wang Yejuan, Li Desheng and P. E. Kloeden. On the asymptotical behavior of nonautonomous dynamical systems. Nonlin. Analysis 59 (2004), 35-53.
27. S. Zelik. Global averaging and parametric resonances in damped semilinear wave equations. University of Poitiers, Department of Mathematics, preprint no. 176 (2003).