A remark on reaction-diffusion equations in unbounded domains

Martino Prizzi

doi:10.3934/dcds.2003.9.281

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2003, Volume 9, Issue 2: 281-286. Doi: 10.3934/dcds.2003.9.281

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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

Received: July 31, 2001

Revised: March 31, 2002

Published: February 2003

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Abstract

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.

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Mathematics Subject Classification: 35K57, 35B40, 35B41.

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