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 Rd. 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 L2 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.