Cahn-Hilliard方程的拟谱逼近的长时间性态

Cahn-Hilliard方程是多年来被广泛关注的热点问题,也以各种方法给出了该方程解的存在性和唯一性等.但在该方程的拟谱逼近中,一般都对相关因子给出了特别的约束.给出了该方程无特别约束条件的半离散显格式及全离散隐格式的Fourier拟谱格式,并证明了该格式全局吸引子的存在性,解的长时间存在性和稳定性,并给出了格式的最优阶误差估计.

The long-time behavior of Fourier pseudo-spectral method of the nonlinear Cahn-Hilliard equation

Cahn-Hilliard equation is a hot problem concerned for a long time. The existence and uniqueness etc of its solution have been given by various methods. However, in Fourier pseudo-spectral methods, related factors must add special constraint condition. The long-time behavior of Fourier pseudo-spectral methods of the semi-discrete and full-discrete of the nonlinear Cahn-Hilliard equation are investigated in no special constraint condition. The existence of global attractor and solutions of a long time and stability are proved for the discrete system. Finally, error bounds of approximation solution are derived.