FINITE DIMENSIONAL BEHAVIOR FOR THE DISSIPATIVE GENERALIZED SYMMETRIC REGULARIZED LONG WAVE EQUATIONS

作     者：SHANGYadong GUOBoling SHANG Yadong (Department of Mathematics, Guangzhou University, Guangzhou 510405, China)QUO Holing (Institute of Applied Physics and Computational Mathematics, P.O.Box 8009, Beijing 100088, China)

作者机构：DepavtmentofMathematicsGuangzhouUniversityGuangzhou510405China InstituteofAppliedPhysicsandComputationalMathematicsP.O.Box8009Beijing100088China 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2003年第16卷第2期

页      面：236-248页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 070201[理学-理论物理] 0701[理学-数学] 0702[理学-物理学] 

基　　金：This research is supported by the National Natural Science Foundation of China(Grant 10271034) 

主　　题：symmetric regularized long wave equation periodic initial value problem global attractors hausdorff dimension fractal dimension 

摘      要：This paper deals with the asymptotic behaviour of solutions for thegeneralized symmetric regularized long wave equations with dissipation term. We first show theexistence of global weak attractors for the periodic initial value problem of this equations in H^2x H^1. And then by an energy equation and an idea of Ghidaglia and Guo, we conclude that the globalweak attractor is actually the global strong attractor for S(t) in H^2 (Ω) x H^1 (Ω). The finitedimensionality of the global attractor is also established.