Existence and finite dimensionality of the global attractor for evolution equations on unbounded domains

AbstractThis paper is devoted to the asymptotic behavior for some evolution equations when the underlying Euclidean domain is unbounded. We present a method that is able to overcome the lack of compactness of the trajectories in such situations, and that allows us to obtain some results on the global attractor similar to those on bounded domains. This method is based on the utilization of an appropriate weight integration function that depends on x and t and becomes effective (in x) for large t's