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2009, 2009(Special): 846-856. doi: 10.3934/proc.2009.2009.846

Exponential attractors for Belousov-Zhabotinskii reaction model

Atsushi Yagi 1, , Koichi Osaki 2, and  Tatsunari Sakurai 3,

1. 

Department of Applied Physics, Osaka University, Suita, Osaka, 565-0871
2. 

Department of Business Adminstration, Ube National College of Technology, Ube, Yamaguchi 755-8555, Japan
3. 

Department of Physics, Chiba University, Chiba 263-8522, Japan

Received  July 2008 Revised  April 2009 Published  September 2009

This paper is concerned with the Belousov-Zhabotinskii reaction model. We consider the reaction-diffusion model due to Keener-Tyson. After constructing a dynamical system, we will construct exponential attractors and will estimate the attractor dimension from below. In particular, it will be shown that, as the excitability $\epsilon > 0$ tends to zero, the attractor dimension tends to infinity, although the exponential attractor can depend on the excitability continuously.
Keywords: Reaction-diffusion model, Belousov-Zhabotinskii reaction, Exponential attractors.
Mathematics Subject Classification: Primary: 37L25; Secondary: 35K57.
Citation: Atsushi Yagi, Koichi Osaki, Tatsunari Sakurai. Exponential attractors for Belousov-Zhabotinskii reaction model. Conference Publications, 2009, 2009 (Special) : 846-856. doi: 10.3934/proc.2009.2009.846
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