关于Benjamin-Bona-Mahony方程在无界域中全局吸引子存在性的注记
A Note to the Existence of Global Attractors for the Benjamin-Bona-Mahony Equation in Unbounded Domains
摘要: 本文证明了广义Benjamin-Bona-Mahony方程在三维通道中全局吸引子的存在性。该文处理了非线性项的增长阶数0 ≤ m < 2的情形，特别是证明解半群的渐近紧性时，运用高阶正则性，将解半群分解成两部分，从而获得解半群的渐近紧性。本文使用了不同的方法得到了证明了Wang-Fussner-Bi (J. Phys. A 40 (2007), no. 34, 10491-10504)中的结果。
Abstract: This paper proves the existence of a global attractor for the generalized Benjamin-Bona-Mahony equation in a three-dimensional channel. The paper deals with the case of the growth order of the nonlinear term 0 ≤ m < 2, especially when proving the asymptotic compactness of the solution semigroup, it decomposes the solution semigroup into two parts by using higher-order regularity, thereby obtaining the asymptotic compactness of the solution semigroup. This paper re-proves the results in Wang-Fussner-Bi (J. Phys. A 40 (2007), no. 34, 10491-10504).
文章引用：徐玉莹. 关于Benjamin-Bona-Mahony方程在无界域中全局吸引子存在性的注记[J]. 应用数学进展, 2025, 14(6): 498-509. https://doi.org/10.12677/aam.2025.146338

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