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About global null controllability of a quasi-static thermoelastic contact system
2005, 2005(Special): 824-832.
doi: 10.3934/proc.2005.2005.824
On the global attractor for the damped Benjamin-Bona-Mahony equation
1. | Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd, Lawrence, KS 66045-7523, United States |
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: 35B4.
Citation:
Milena Stanislavova. On the global attractor for the damped Benjamin-Bona-Mahony equation. Conference Publications,
2005, 2005
(Special)
: 824-832.
doi: 10.3934/proc.2005.2005.824
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