English

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

Analysis of PDEs 2009-10-20 v1 Dynamical Systems

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 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.

Keywords

Cite

@article{arxiv.0910.3588,
  title  = {Attractors for nonlinear reaction-diffusion systems in unbounded domains via the method of short trajectories},
  author = {Maurizio Grasselli and Dalibor Pražák and Giulio Schimperna},
  journal= {arXiv preprint arXiv:0910.3588},
  year   = {2009}
}