Exponential attractors for Belousov-Zhabotinskii reaction model

Atsushi Yagi; Koichi Osaki; Tatsunari Sakurai

doi:10.3934/proc.2009.2009.846

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2009, Volume 2009: 846-856. Doi: 10.3934/proc.2009.2009.846 open access

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Exponential attractors for Belousov-Zhabotinskii reaction model

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
3.
Department of Physics, Chiba University, Chiba 263-8522

Received: June 30, 2008

Revised: March 31, 2009

Published: August 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 37L25; Secondary: 35K57.

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