Attractor for a Strongly Damped Lattice System with Nonlinear Damping

Abstract

We prove the existence of a global attractor of a strongly damped lattice system with the damped force q(u_i) u_i+β(u_i) where the coupled operator is nonnegative definite symmetric and obtain an upper Hausdorff dimension of the global attractor, which keeps bounded for large damping.