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March  2003, 9(2): 281-286. doi: 10.3934/dcds.2003.9.281

A remark on reaction-diffusion equations in unbounded domains

Martino Prizzi 1,

1. 

Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, Via Valerio 12/b, 34100 Trieste, Italy

Received  August 2001 Revised  April 2002 Published  December 2002

We prove the existence of a compact $(L^2-H^1)$ attractor for a reaction-diffusion equation in $R^N$. This improves a previous result of B. Wang concerning the existence of a compact $(L^2-L^2)$ attractor for the same equation.
Keywords: attractor., asymptotic compactness, Reaction-di usion equation.
Mathematics Subject Classification: 35K57, 35B40, 35B4.
Citation: Martino Prizzi. A remark on reaction-diffusion equations in unbounded domains. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 281-286. doi: 10.3934/dcds.2003.9.281
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