非自治Ginzburg-Landau方程的有限维行为  

FINITE DIMENSIONAL BEHAVIOR FOR THE NONAUTONOMOUS GINZBURG-LANDAU EQUATION

作　　者：吴书印[1] 赵怡[2] 

机构地区：[1]中山大学计算机科学系,广州510275 [2]中山大学数学系,广州510275

出　　处：《数学年刊（A辑）》2004年第4期511-522,共12页Chinese Annals of Mathematics

摘　　要：本文研究Ω R^n(n=1,2,3)上具有几乎周期外力的非自治Ginzburg-Landau方程的有限维行为。证明了非自治Ginzburg-Landau系统存在紧的一致吸引子A_1。当外力是时间拟周期时,得到了吸引子A_1的Hausdorff维数的上界估计,当外力是时间周期时,证明了吸引子里一定含有周期解,而且当耗散系数λ满足适当条件时,系统在空间H=L^2(Q)上存在唯一周期解,该周期解指数吸引H中的任何有界集。In case of Ω R^n (n=1, 2, 3), the authors prove the existence of the uniform attractor A_1 for the nonautonomous Ginzburg-Landau system with external force f=f(x, t) of almost period (a.p.) in time. When the external force f is a quasiperiodic (q.p.) function in time, the authors present the upper bound of the Hausdorff dimension of the attractor A_1. Further, when the external force f is a periodic function in time, it is shown that there are periodic solutions in the attractor, and if the dissipative parameter is in certain range, the system has a unique periodic solution in H, which attracts any bounded set exponentially.

关 键 词：非自治G-L方程 一致吸引子 HAUSDORFF维数 周期解 周期吸引子 

分 类 号：O175.29[理学—数学]