American Institute of Mathematical Sciences

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2009, 2009(Special): 857-868. doi: 10.3934/proc.2009.2009.857

Asymptotical dynamics of the modified Schnackenberg equations

Yuncheng You 1,

1. 

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

Received  June 2008 Revised  February 2009 Published  September 2009

The existence of a global attractor in the $L^2$ product phase space for the solution semiflow of the modified Schnackenberg equations with the Dirichlet boundary condition on a bounded domain of space dimension $n\le 3$ is proved. This reaction-diffusion system features two pairs of oppositely-signed nonlinear terms so that the dissipative sign-condition is not satisfied. The proof features two types of rescaling and grouping estimation in showing the absorbing property and the uniform smallness in proving the asymptotical compactness by the approach of a new decomposition.
Keywords: absorbing set, Schnackenberg equation, asymptotical compactness, global dynamics, global attractor.
Mathematics Subject Classification: 37L30, 35B40, 35B41, 35K55, 35K57, 35Q80.
Citation: Yuncheng You. Asymptotical dynamics of the modified Schnackenberg equations. Conference Publications, 2009, 2009 (Special) : 857-868. doi: 10.3934/proc.2009.2009.857
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