American Institute of Mathematical Sciences

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2007, 2007(Special): 334-343. doi: 10.3934/proc.2007.2007.334

Uniform estimate of dimension of the global attractor for a semi-discretized chemotaxis-growth system

Messoud Efendiev 1, , Etsushi Nakaguchi 2, and  Wolfgang L. Wendland 3,

1. 

Department of Mathematics, Technical University of Muinch, Boltzmannstrasse 3, 85747 Garching, Germany
2. 

Graduate School of Information Science and Technology, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan
3. 

Department of Mathematics, University of Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany

Received  August 2006 Revised  January 2007 Published  September 2007

We study a finite-element approximation of the chemotaxis-growth system. We establish dimension estimate of global attractors for the approximate systems. Our results show that the estimates are uniform with respect to the discretization parameter and polynomial order with respect to the chemotactic coefficient in the equation.We especially emphasize that, this is just the same order (polynomial) as for the original system obtained in the preceding papers [Adv.Math.Sci.Appl. Part I and II].
Keywords: finite-element approximation, Dimension of global attractor, chemotaxis-growth system..
Mathematics Subject Classification: Primary: 37L30, 65M60; Secondary: 35K57, 92C1.
Citation: Messoud Efendiev, Etsushi Nakaguchi, Wolfgang L. Wendland. Uniform estimate of dimension of the global attractor for a semi-discretized chemotaxis-growth system. Conference Publications, 2007, 2007 (Special) : 334-343. doi: 10.3934/proc.2007.2007.334
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