Abstract
We consider reaction-diffusion systems in unbounded domains, prove the existence of expotential attractors for such systems, and estimate their fractal dimension. The essential difference with the case of a bounded domain studied before is the continuity of the spectrum of the linear part of the equations. This difficulty is overcome by systematic use of weighted Sobolev spaces.
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Babin, A., Nicolaenko, B. Exponential attractors of reaction-diffusion systems in an unbounded domain. J Dyn Diff Equat 7, 567–590 (1995). https://doi.org/10.1007/BF02218725
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DOI: https://doi.org/10.1007/BF02218725