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April, 2011 Exponential attractors for non-autonomous dissipative system
Messoud EFENDIEV, Yoshitaka YAMAMOTO, Atsushi YAGI
J. Math. Soc. Japan 63(2): 647-673 (April, 2011). DOI: 10.2969/jmsj/06320647


In this paper we will introduce a version of exponential attractor for non-autonomous equations as a time dependent set with uniformly bounded finite fractal dimension which is positively invariant and attracts every bounded set at an exponential rate. This is a natural generalization of the existent notion for autonomous equations. A generation theorem will be proved under the assumption that the evolution operator is a compact perturbation of a contraction. In the second half of the paper, these results will be applied to some non-autonomous chemotaxis system.


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Messoud EFENDIEV. Yoshitaka YAMAMOTO. Atsushi YAGI. "Exponential attractors for non-autonomous dissipative system." J. Math. Soc. Japan 63 (2) 647 - 673, April, 2011.


Published: April, 2011
First available in Project Euclid: 25 April 2011

zbMATH: 1218.37111
MathSciNet: MR2793113
Digital Object Identifier: 10.2969/jmsj/06320647

Primary: 37L25
Secondary: 35K57

Keywords: chemotaxis model , exponential attractors , non-autonomous dynamical system

Rights: Copyright © 2011 Mathematical Society of Japan


Vol.63 • No. 2 • April, 2011
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