Global attractor of the Gray-Scott equations

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

Global attractor of the Gray-Scott equations

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

Received June 2007 Revised September 2007 Published April 2008

Abstract
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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 & Applied Analysis, 2008, 7 (4) : 947-970. doi: 10.3934/cpaa.2008.7.947

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