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March  2009, 2(1): 55-66. doi: 10.3934/dcdss.2009.2.55

The existence and the structure of uniform global attractors for nonautonomous Reaction-Diffusion systems without uniqueness

Alexey Cheskidov 1, and  Songsong Lu 2,

1. 

Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 S Morgan St, Chicago, IL 60607-7045, United States
2. 

Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China

Received  February 2008 Revised  December 2008 Published  January 2009

We study the uniform global attractor for a general nonautonomous reaction-diffusion system without uniqueness using a new developed framework of an evolutionary system. We prove the existence and the structure of a weak uniform (with respect to a symbol space) global attractor $\mathcal A$. Moreover, if the external force is normal, we show that this attractor is in fact a strong uniform global attractor. The existence of a uniform (with respect to the initial time) global attractor $\mathcal A^0$ also holds in this case, but its relation to $\mathcal A$ is not yet clear due to the non-uniqueness feature of the system.
Keywords: normal symbol., reaction-diffusion system, evolutionary system, uniform global attractor.
Mathematics Subject Classification: 35B40, 35B4.
Citation: Alexey Cheskidov, Songsong Lu. The existence and the structure of uniform global attractors for nonautonomous Reaction-Diffusion systems without uniqueness. Discrete & Continuous Dynamical Systems - S, 2009, 2 (1) : 55-66. doi: 10.3934/dcdss.2009.2.55
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