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