Exponential attractors for second order lattice dynamical systems (Q1012839)

Lattice dynamical systems are infinite systems of ODEs or difference equations, indexed by points in a lattice, such as the \(k\)-dimensional integer lattice \(\mathbb{Z}^k\). In the article [J. Math. Anal. Appl. 339, No. 1, 217--224 (2008; Zbl 1127.37051)], the author had introduced the exponential attractors for LDS, where a first order system has been presented. Here he proves the existence of an exponential attractors for the solution semigroup of a second order LDS acting on an closed bounded positively invariant set in the infinite dimensional Hilbert space \(l^2\times l^2\).