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We consider a nonlinear reaction-diffusion equation settled on the wholeeuclidean space. We prove the well-posedness of the corresponding Cauchyproblem in a general functional setting, namely, when the initial datum isuniformly locally bounded in L^2. Then we adapt the short trajectory method toestablish the existence of the global attractor and, if the space dimension isat most 3, we also find an upper bound of its Kolmogorov's entropy.

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