Special Session 29: Stochastic and deterministic dynamical systems and applications
Contents
In this talk results on the existence of a pullback exponential attractor for an evolution process are presented. This positively invariant family of compact subsets has a uniformly bounded fractal dimension and pullback attracts all bounded subsets at an exponential rate. The novelty is that the construction admits the exponential growth in the past of the sets forming the family and generalizes the known approaches. It also allows to substitute the smoothing property by a weaker requirement without auxiliary spaces. The theory is illustrated with examples of nonautonomous reaction-diffusion equations including the time-dependent version of the well-known Chafee-Infante equation.