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On the Existence of the Compact Global Attractor for Semilinear Reaction Diffusion Systems on RN

✍ Scribed by Sandro Merino

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 870 KB
Volume: 132
Category: Article
ISSN: 0022-0396
DOI: 10.1006/jdeq.1996.0172

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✦ Synopsis

We show that a class of reaction diffusion systems on R N generates an asymptotically compact semiflow on the Banach space of bounded uniformly continuous functions. If such a semiflow is dissipative, then a unique, non-empty, compact minimal attractor is known to exist. We apply this abstract result to obtain the existence of the compact minimal attractor for reaction diffusion systems on R N that contain appropriate weight functions. We also state conditions, which guarantee that the attractor has finite Hausdorff-dimension.

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