Dimension estimate of the exponential attractor for the chemotaxis-growth system

Messoud Efendiev; Michael Kläre; Rupert Lasser

doi:10.1002/mma.801

Dimension estimate of the exponential attractor for the chemotaxis-growth system

Messoud Efendiev
, Michael Kläre
, Rupert Lasser

Department of Mathematics

Technical University of Munich

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We consider a chemotaxis-growth model which takes into account diffusion, chemotaxis, production of chemical substance, and growth. We present estimates from above and below of the fractal dimension dim ̄ of the exponential attractor ̄ in terms of the coefficients of the system. Comparisons are made between the sizes of the global and exponential attractors. Numerical simulations are presented which confirm the analytical results obtained.

Original language	English
Pages (from-to)	579-594
Number of pages	16
Journal	Mathematical Methods in the Applied Sciences
Volume	30
Issue number	5
DOIs	https://doi.org/10.1002/mma.801
State	Published - 25 Mar 2007

Keywords

Chemotaxis-growth model
Diffusion
Fractal dimension
Global and exponential attractors
Numerical results

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10.1002/mma.801

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AU - Efendiev, Messoud

AU - Kläre, Michael

AU - Lasser, Rupert

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Y1 - 2007/3/25

N2 - We consider a chemotaxis-growth model which takes into account diffusion, chemotaxis, production of chemical substance, and growth. We present estimates from above and below of the fractal dimension dim ̄ of the exponential attractor ̄ in terms of the coefficients of the system. Comparisons are made between the sizes of the global and exponential attractors. Numerical simulations are presented which confirm the analytical results obtained.

AB - We consider a chemotaxis-growth model which takes into account diffusion, chemotaxis, production of chemical substance, and growth. We present estimates from above and below of the fractal dimension dim ̄ of the exponential attractor ̄ in terms of the coefficients of the system. Comparisons are made between the sizes of the global and exponential attractors. Numerical simulations are presented which confirm the analytical results obtained.

KW - Chemotaxis-growth model

KW - Diffusion

KW - Fractal dimension

KW - Global and exponential attractors

KW - Numerical results

UR - https://www.scopus.com/pages/publications/33847707941

U2 - 10.1002/mma.801

DO - 10.1002/mma.801

M3 - Article

AN - SCOPUS:33847707941

SN - 0170-4214

VL - 30

SP - 579

EP - 594

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 5

ER -

Dimension estimate of the exponential attractor for the chemotaxis-growth system

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Keywords

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