, Volume 7, Issue 4, pp 567-590

Exponential attractors of reaction-diffusion systems in an unbounded domain

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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.