Asymptotical dynamics of Selkov equations

Pages: 193 - 219, Volume 2, Issue 1, March 2009

doi:10.3934/dcdss.2009.2.193       Abstract        Full Text (310.6K)       Related Articles

Yuncheng You - Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, United States (email)

Abstract: 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.

Keywords:  Selkov equation, asymptotical dynamics, global attractor, absorbing set, asymptotic compactness, fractal dimension.
Mathematics Subject Classification:  Primary: 37L30; Secondary: 35B40, 35B41, 35K55, 35K57, 35Q80.

Received: March 2008;      Revised: July 2008;      Published: January 2009.