三维非线性Sobolev-Galpern方程有限差分逼近的长时间行为(英文)  

Long time behavior of finite difference approximation to the 3D nonlinear Sobolev-Galpern equation

作　　者：张磊[1] 王珏[2] 张法勇[1] 

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080 [2]哈尔滨工程大学理学院,哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2010年第4期440-445,共6页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the Science Foundation of the Education Committee of Heilongjiang Province (11541269);the Youth Foundation of Heilongjiang University (QL200804)

摘　　要：研究三维非线性Sobolev-Galpern方程Dirichlet初值问题的一个全离散有限差分格式。利用离散空间泛函分析和能量估计的方法证明了此数值格式的唯一可解性,同时得到了此差分格式的长时间的稳定性和收敛性。进一步,证明了离散动力系统整体吸引子的存在性以及离散动力系统的上半连续性。上述结果说明该数值离散格式可有效地模拟相应的无穷维动力系统。A fully discrete difference scheme to the 3D nonlinear Sobolev-Galpern equation with Dirichlet initial-value problem is presented.The unique solvability of numerical solution is shown by using discrete space functional analysis and energy estimate method.The long-time stability and convergence of the scheme are proved.Furthermore,the existence of global attractor for the discrete dynamical system and the upper semicontinuity d（Ah,τ,A）→0 are proved.Results show that the difference scheme can effectively simulate the infinite dimensional dynamical systems.

关 键 词：非线性SOBOLEV-GALPERN方程 有限差分格式 唯一可解性 全局吸引子 长时间收敛性及稳定性 

分 类 号：O177.1[理学—数学]