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.

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

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