Global attractor of the Gray-Scott equations

Yuncheng You

doi:10.3934/cpaa.2008.7.947

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2008, Volume 7, Issue 4: 947-970. Doi: 10.3934/cpaa.2008.7.947

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Global attractor of the Gray-Scott equations

Yuncheng You^1,

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

Received: May 31, 2007

Revised: August 31, 2007

Published: June 2008

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Abstract

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.

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

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