Asymptotic dynamics of reversible cubic autocatalytic reaction-diffusion systems

Yuncheng You

doi:10.3934/cpaa.2011.10.1415

Article Contents

2011, Volume 10, Issue 5: 1415-1445. Doi: 10.3934/cpaa.2011.10.1415

This issue Previous Article Nonautonomous resonant periodic systems with indefinite linear part and a nonsmooth potential Next Article Stability analysis of inhomogeneous equilibrium for axially and transversely excited nonlinear beam

Asymptotic dynamics of reversible cubic autocatalytic reaction-diffusion systems

Yuncheng You^1,

1.
Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620

Received: May 2009

Revised: March 2010

Published: September 2011

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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:

Mathematics Subject Classification: Primary: 37L30; Secondary: 35B40, 35B41, 35K55, 35K57, 35Q80.

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