Asymptotic dynamics of reversible cubic autocatalytic reaction-diffusion systems

Pages: 1415 - 1445, Volume 10, Issue 5, September 2011

doi:10.3934/cpaa.2011.10.1415       Abstract        References        Full Text (542.3K)       Related Articles

Yuncheng You - Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, United States (email)

Abstract: In this paper we prove the existence of a global attractor, an $(H,E)$ global attractor, and an exponential attractor for the cubic autocatalytic reaction-diffusion systems represented by the reversible Gray-Scott equations. The two pairs of oppositely signed nonlinear terms feature the challenge in conducting various estimates. A new rescaling and grouping estimation method is introduced and combined with the other approaches to achieve the proof of dissipation, asymptotic compactness, and discrete squeezing property in all the stages.

Keywords:  Reversible reaction-diffusion system, cubic autocatalysis, Gray-Scott equations, asymptotic dynamics, global attractor, exponential attractor.
Mathematics Subject Classification:  Primary: 37L30; Secondary: 35B40, 35B41, 35K55, 35K57, 35Q80.

Received: May 2009;      Revised: March 2010;      Published: April 2011.

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