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Zbl 1088.37005
Efendiev, M.; Zelik, S.; Miranville, A.
Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems. (English)
[J] Proc. R. Soc. Edinb., Sect. A, Math. 135, No. 4, 703-730 (2005). ISSN 0308-2105; ISSN 1473-7124/e

Summary: We suggest a new explicit algorithm allowing us to construct exponential attractors which are uniformly Hölder continuous with respect to the variation of the dynamical system in some natural large class. Moreover, we extend this construction to nonautonomous dynamical systems (dynamical processes) treating in that case the exponential attractor as a uniformly exponentially attracting, finite-dimensional and time-dependent set in the phase space. In particular, this result shows that, for a wide class of nonautonomous equations of mathematical physics, the limit dynamics remains finite-dimensional no matter how complicated the dependence of the external forces on time is. We illustrate the main results on the model example of a nonautonomous reaction-diffusion system in a bounded domain.

MSC 2000:: *37B55 Nonautonomous dynamical systems
37L30 Attractors and their dimensions
37C70 Attractors and repellers, topological structure
35K57 Reaction-diffusion equations
35B41 Attractors

Keywords: exponential attractors; non-autonomous equations; reaction-diffusion system

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