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