# American Institute of Mathematical Sciences

March  2009, 2(1): 193-219. doi: 10.3934/dcdss.2009.2.193

## Asymptotical dynamics of Selkov equations

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

Received  March 2008 Revised  July 2008 Published  January 2009

The existence of a global attractor for the solution semiflow of Selkov equations with Neumann boundary conditions on a bounded domain in space dimension $n\le 3$ is proved. This reaction-diffusion system features the oppositely-signed nonlinear terms so that the dissipative sign-condition is not satisfied. The asymptotical compactness is shown by a new decomposition method. It is also proved that the Hausdorff dimension and fractal dimension of the global attractor are finite.
Citation: Yuncheng You. Asymptotical dynamics of Selkov equations. Discrete & Continuous Dynamical Systems - S, 2009, 2 (1) : 193-219. doi: 10.3934/dcdss.2009.2.193
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