Attractors for nonlinear reaction–diffusion systems in unbounded domains via the method of short trajectories

Abstract

We consider a nonlinear reaction–diffusion equation on the whole space R d . We prove the well-posedness of the corresponding Cauchy problem in a general functional setting, namely, when the initial datum is uniformly locally bounded in L 2 only. Then we adapt the short trajectory method to establish the existence of the global attractor and, if d ⩽ 3 , we find an upper bound of its Kolmogorov's ε-entropy.