On the global attractor for the damped Benjamin-Bona-Mahony equation

Pages: 824 - 832, Issue Special, August 2005

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Milena Stanislavova - Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd, Lawrence, KS 66045-7523, United States (email)

Abstract: We present a new necessary and sufficient condition to verify the asymptotic compactness of an evolution equation defined in an unbounded domain, which involves the Littlewood-Paley projection operators. We then use this condition to prove the existence of an attractor for the damped \bbme in the phase space $H^1({\bf R})$ by showing the solutions are point dissipative and asymptotically compact. Moreover the attractor is in fact smoother and it belongs to $H^{3/2-\ve}$ for every $\ve>0$.

Keywords:  Keywords and Phrases
Mathematics Subject Classification:  Primary: 35B40; Secondary: 35B41.

Received: September 2004;      Revised: April 2005;      Published: September 2005.