Exponential attractors for non-autonomous dissipative system

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  • Efendiev Messoud
    Helmholtz-Zentrum München, Institute of Biomathematics and Biometry
  • Yamamoto Yoshitaka
    Department of Information Physical Science, Graduate School of Information Science and Technology, Osaka University
  • Yagi Atsushi
    Department of Applied Physics, Graduate School of Engineering, Osaka University

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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.

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