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July  2008, 7(4): 947-970. doi: 10.3934/cpaa.2008.7.947

Global attractor of the Gray-Scott equations

Yuncheng You 1,

1. 

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

Received  June 2007 Revised  September 2007 Published  April 2008

In this work the existence of a global attractor for the solution semiflow of the Gray-Scott equations with the Neumann boundary conditions on bounded domains of space dimensions $n\leq 3$ is proved. This reaction-diffusion system does not have dissipative property inherently due to the oppositely signed nonlinearity. The asymptotical compactness is shown by a new decomposition method. It is also proved that the Hausdorff dimension and the fractal dimension of the global attractor are finite.
Keywords: global attractor, fractal dimension., global dynamics, asymptotic compactness, Gray-Scott equation, absorbing set.
Mathematics Subject Classification: 37L30, 35B40, 35B41, 35K55, 35K57, 35Q8.
Citation: Yuncheng You. Global attractor of the Gray-Scott equations. Communications on Pure and Applied Analysis, 2008, 7 (4) : 947-970. doi: 10.3934/cpaa.2008.7.947
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