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November  2010, 14(4): 1671-1688. doi: 10.3934/dcdsb.2010.14.1671

Dynamics of three-component reversible Gray-Scott model

Yuncheng You 1,

1. 

Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, United States

Received  August 2009 Revised  January 2010 Published  August 2010

The existence of a global attractor for the solution semiflow of a three-component reversible Gray-Scott system with Neumann boundary condition on a bounded domain of space dimension $n\le 3$ is proved. The methodology features the re-scaling and grouping estimation to overcome the difficulty of non-dissipative coupling of three variables and the coefficient barrier. It is also shown that the global attractor turns out to be an $(H, E)$ global attractor.
Keywords: asymptotic compactness., Reversible Gray-Scott system, global attractor, asymptotic dynamics, absorbing set.
Mathematics Subject Classification: Primary: 37L30; Secondary: 35B40, 35B41, 35K55, 35K57, 35Q80, 35Q9.
Citation: Yuncheng You. Dynamics of three-component reversible Gray-Scott model. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1671-1688. doi: 10.3934/dcdsb.2010.14.1671
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