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

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 the d < 4, we find an upper bound of its Kolmogorov’s epsilon-entropy