Attractor and dimension for discretization of a damped wave equation with periodic nonlinearity (Q1590111)

The paper is devoted to the discretization of the following damped wave equation with periodic nonlinearity \[ \frac{\partial^2u}{\partial t^2}+\alpha \frac{\partial u}{\partial t}- \Delta u+g(u)=f, \quad x\in \Omega,\;t\geq 0, \tag{1} \] with the periodic boundary conditions. The author proves the existence of a global attractor for the discretized version of (1) and estimates its Hausdorff dimension. The estimate obtained for Hausdorff dimension is independent of the mesh sizes and the space dimension and remains small for large damping.