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

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

2009-10-19

arxiv.org/abs/0910.3588v1

Mathematics

Analysis of PDEs

Scientific paper

We consider a nonlinear reaction-diffusion equation settled on the whole euclidean space. 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. Then we adapt the short trajectory method to establish the existence of the global attractor and, if the space dimension is at most 3, we also find an upper bound of its Kolmogorov's entropy.

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