On the global attractor for the damped Benjamin-Bona-Mahony equation
On the global attractor for the damped Benjamin-Bona-Mahony equation
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DOI：
10.3934/proc.2005.2005.824
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发表时间：
2005-09
期刊：
影响因子：
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通讯作者：
M. Stanislavova
中科院分区：
文献类型：
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作者：
M. Stanislavova
给出了无界区域上发展方程渐近紧性的一个新的充分必要条件，该条件涉及Littlewood-Paley投影算子。然后，我们使用这个条件来证明阻尼\bbme在相空间$H^1（{\bfR}）$中的吸引子的存在性，通过显示解是点耗散的和渐近紧的。此外，吸引子实际上更平滑，并且对于每个$\ve>0$，它都属于$H^{3/2-\ve}$。
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 $\ve>0$.