Attractors for autonomous and nonautonomous 3D Benjamin-Bona-Mahony equations
Attractors for autonomous and nonautonomous 3D Benjamin-Bona-Mahony equations
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DOI：
10.1016/j.amc.2015.10.086
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发表时间：
2016-02
期刊：
影响因子：
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通讯作者：
Jum‐Ran Kang
中科院分区：
文献类型：
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作者：
Jum‐Ran Kang
本文考虑三维Benjamin-Bona-Mahony方程在自治和非自治情形下的长时间行为。针对三维Benjamin-Bona-Mahony方程组渐近正则性证明中的困难，引入了一种有效的分解方法。对于自治情形，证明了当外部强迫属于V ′时全局吸引子的存在性。对于非自治情形，我们只假设f（x，t）是平移有界的而不是平移紧的.利用这些分解方法，我们证明了三维Benjamin-Bona-Mahony方程解的渐近正则性，并得到了一致吸引子的存在性。
In this paper we consider the long time behavior of the three dimensional Benjamin–Bona–Mahony equations for the autonomous and nonautonomous cases. A useful decomposition method is introduced to overcome the difficulties in proving the asymptotical regularity of the 3D Benjamin–Bona–Mahony equations. For the autonomous case, we prove the existence of global attractor when the external forcing belongs toV′. For the nonautonomous case, we only assume thatf(x, t) is translation bounded instead of translation compact. By means of this useful decomposition methods, we prove the asymptotic regularity of solutions of 3D Benjamin–Bona–Mahony equations and also obtain the existence of the uniform attractor.