A Note to the Existence of Global Attractors for the Benjamin-Bona-Mahony Equation in Unbounded Domains

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 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).