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LOWER ESTIMATE OF THE ATTRACTOR DIMENSION FOR A CHEMOTAXIS GROWTH SYSTEM

Published online by Cambridge University Press:  25 October 2006

MASASHI AIDA ,
TOHRU TSUJIKAWA ,
MESSOUD EFENDIEV ,
ATSUSHI YAGI  and
MASAYASU MIMURA
MASASHI AIDA
Affiliation:
Department of Applied Physics, Osaka University, Suita Osaka 565-0871, Japan
TOHRU TSUJIKAWA
Affiliation:
Faculty of Engineering, Miyazaki University, Miyazaki 889-2192, Japan
MESSOUD EFENDIEV
Affiliation:
University of Stuttgart, Mathematisches Institut A, Pfaffenwaldring 57, 70569 Stuttgart, Germany
ATSUSHI YAGI
Affiliation:
Department of Applied Physics, Osaka University, Suita Osaka 565-0871, Japanyagi@ap.eng.osaka-u.ac.jp
MASAYASU MIMURA
Affiliation:
Department of Mathematics, Meiji University, Kawasaki, Kanagawa 214-8571, Japan
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Abstract

This paper estimates from below the attractor dimension of the dynamical system determined from a chemotaxis growth model which was presented by Mimura and Tsujikawa. It is already known that the dynamical system has exponential attractors and it is also known by numerical computations that the model contains various pattern solutions. This paper is then devoted to estimating the attractor dimension from below and in fact to showing that, as the parameter of chemotaxis increases and tends to infinity, so does the attractor dimension. Such a result is in a good correlation with the numerical results.

Keywords

37L30 (primary)35K5792D40 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 74 , Issue 2 , October 2006 , pp. 453 - 474
Copyright
The London Mathematical Society 2006

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