Attractor of a semi-discrete Benjamin-Bona-Mahony equation on R-1

作者：Zhu Chaosheng^*

来源：Annales Polonici Mathematici, 2015, 115(3): 219-234.

DOI：10.4064/ap115-3-2

• Benjamin-Bona-Mahony equation
• Crank-Nicolson scheme
• global attractor
• regularity
• fractal dimension

This paper is concerned with the study of the large time behavior and especially the regularity of the global attractor for the semi-discrete in time Crank-Nicolson scheme to discretize the Benjamin-Bona-Mahony equation on R-1. Firstly, we prove that this semi-discrete equation provides a discrete infinite-dimensional dynamical system in H-1 (R-1). Then we prove that this system possesses a global attractor A(tau) in H-1(R-1). In addition, we show that the global attractor A(tau) is regular, i.e., A(tau) is actually included, bounded and compact in H-2(R-1). Finally, we estimate the finite fractal dimensions of A,

• 出版日期2015
• 单位西南大学