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DIMENSION ESTIMATE OF THE EXPONENTIAL ATTRACTOR FOR THE CHEMOTAXIS–GROWTH SYSTEM*

Published online by Cambridge University Press:  01 September 2008

MESSOUD EFENDIEV ,
ETSUSHI NAKAGUCHI  and
KOICHI OSAKI
MESSOUD EFENDIEV
Affiliation:
Department of Mathematics, Technical University of Munich, Boltzmannstrasse 3, 85747 Garching, Germany e-mail: messoud.efendiyev@gsf.de
ETSUSHI NAKAGUCHI
Affiliation:
Graduate School of Information Science and Technology, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan e-mail: nakaguti@ist.osaka-u.ac.jp
KOICHI OSAKI
Affiliation:
Department of Business Administration, Ube National College of Technology, 2-14-1 Tokiwadai, Ube, Yamaguchi 755-8555, Japan e-mail: osaki@ube-k.ac.jp
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Abstract

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In this paper, we study an upper bound of the fractal dimension of the exponential attractor for the chemotaxis–growth system in a two-dimensional domain. We apply the technique given by Eden, Foias, Nicolaenko and Temam. Our results show that the bound is estimated by polynomial order with respect to the chemotactic coefficient in the equation similar to our preceding papers.

Keywords

35K1535K5737L30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 3 , September 2008 , pp. 483 - 497
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

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