Premium
Dimension estimate of the exponential attractor for the chemotaxis‐growth system
Author(s) -
Efendiev Messoud,
Kläre Michael,
Lasser Rupert
Publication year - 2006
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.801
Subject(s) - attractor , mathematics , exponential growth , chemotaxis , dimension (graph theory) , exponential function , fractal dimension , diffusion , mathematical analysis , fractal , statistical physics , pure mathematics , physics , thermodynamics , chemistry , biochemistry , receptor
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. Copyright © 2006 John Wiley & Sons, Ltd.