Abstract and Applied Analysis
Volume 2005 (2005), Issue 6, Pages 655-671
Global attractor for the lattice dynamical system of a nonlinear Boussinesq equation
Department of Mathematics, University of Jordan, Amman 11942, Jordan
Received 28 April 2004
Copyright © 2005 Ahmed Y. Abdallah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We will study the lattice dynamical system of a nonlinear Boussinesq equation. Our objective is to explore the existence of the global attractor for the solution semiflow of the introduced lattice system and to investigate its upper semicontinuity with respect to a sequence of finite-dimensional approximate systems. As far as we are aware, our result here is the first concerning the lattice dynamical system corresponding to a differential equation of second order in time variable and fourth order in spatial variable with nonlinearity involving the gradients.