Benjamin-Bona-Mahony 方程在三维通道中的全局吸引子存在性

数学物理学报 ›› 2026, Vol. 46 ›› Issue (3): 1015-1024.

Benjamin-Bona-Mahony 方程在三维通道中的全局吸引子存在性

万灵(), 徐玉莹(), 张腾飞^*()

中国地质大学数学与物理学院武汉 430074

收稿日期:2024-12-01 修回日期:2025-07-19 出版日期:2026-06-26 发布日期:2026-06-16
通讯作者: 张腾飞 E-mail:wanling@cug.edu.cn;xuyuyingyys66@cug.edu.cn;zhangtf@cug.edu.cn
作者简介:万灵, E-mail:wanling@cug.edu.cn;
徐玉莹, E-mail:xuyuyingyys66@cug.edu.cn
基金资助:
国家自然科学基金(12371228);广东省基础与应用基础研究基金(2024A1515011040)

Existence of Global Attractors of the Benjamin-Bona-Mahony Equation in Three-Dimensional Channel

Ling Wan(), Yuying Xu(), Tengfei Zhang^*()

School of Mathematics and Physics, China University of Geosciences, Wuhan 430074

Received:2024-12-01 Revised:2025-07-19 Online:2026-06-26 Published:2026-06-16
Contact: Tengfei Zhang E-mail:wanling@cug.edu.cn;xuyuyingyys66@cug.edu.cn;zhangtf@cug.edu.cn
Supported by:
NSFC(12371228);Guangdong Basic and Applied Basic Research Foundation(2024A1515011040)

摘要/Abstract

摘要：

该文证明了广义 Benjamin-Bona-Mahony 方程在三维通道区域中的全局吸引子存在性. 该文主要处理非线性项的增长性阶数 $m=2$ 的情形, 推广了此前 Wang-Fussner-Bi [Wang B, Fussner D W, Bi C. J Phys A, 2007, 40(34): 10491-10504] 中的结果. 特别是证明解半群的渐近紧性时, 该文是首先证明了其弱连续性, 其次结合能量方程方法证明了相应范数的收敛性.

关键词: Benjamin-Bona-Mahony 方程, 全局吸引子, 渐近紧性, 弱连续.

Abstract:

This article establishes the existence of global attractors for the (generalized) Benjamin-Bona-Mahony equation in a three-dimensional channel, when the nonlinear term satisfies the growth condition of order $m=2$, which extends the result obtained by Wang-Fussner-Bi [Wang B, Fussner D W, Bi C. J Phys A, 2007, 40(34): 10491-10504]. In particular, in order to prove the asymptotic compactness of the solution semigroup, we prove firstly the weak continuity property, and secondly the convergence in norm by taking advantage of the energy equation method.

Key words: Benjamin-Bona-Mahony equation, global attractor, asymptotic compactness, weak continuity.

中图分类号:

O175.29

万灵, 徐玉莹, 张腾飞. Benjamin-Bona-Mahony 方程在三维通道中的全局吸引子存在性[J]. 数学物理学报, 2026, 46(3): 1015-1024.

Ling Wan, Yuying Xu, Tengfei Zhang. Existence of Global Attractors of the Benjamin-Bona-Mahony Equation in Three-Dimensional Channel[J]. Acta mathematica scientia,Series A, 2026, 46(3): 1015-1024.

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