Exponential attractors for Belousov-Zhabotinskii reaction model. (English) Zbl 1189.37084

Yagi, Atsushi; Osaki, Koichi; Sakurai, Tatsunari

Discrete Contin. Dyn. Syst. 2009, Suppl., 846-856 (2009).

Summary: 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 \(\varepsilon > 0\) tends to zero, the attractor dimension tends to infinity, although the exponential attractor can depend on the excitability continuously.

MSC:

37L25	Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems
35K57	Reaction-diffusion equations

Keywords:

Belousov-Zhabotinskii reaction; reaction-diffusion model; exponential attractors