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

2009/10/19 by Maurizio Grasselli, Grasselli, Maurizio, Dalibor Pražák +3
Mathematics · #35B41 #35K57 #92D25 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #math.AP #math.DS #msc:35B41 #msc:35K57 #msc:92D25

paper · pdf · doi:10.48550/arxiv.0910.3588

arxiv created 2009/10/19 · arxiv updated 2009/12/01

Abstract

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 L². 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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