带可加噪声的非自治随机Boussinesq格点方程的随机吸引子  

Random Attractor for Non-Autonomous Stochastic Boussinesq Lattice Equations with Additive White Noises

作　　者：赵敏 周盛凡[2] Zhao Min;Zhou Shengfan(College of Mathematics,Physics and Electronic Information Engineering,Wenzhou University,Zhejiang Wenzhou 325035;College of Mathematics,Physics and Information Engineering,Zhejiang Normal University,Zhejiang Jinhua 321004)

机构地区：[1]温州大学数理与电子信息工程学院,浙江温州325035 [2]浙江师范大学数理与信息工程学院,浙江金华321004

出　　处：《数学物理学报（A辑）》2018年第5期924-940,共17页Acta Mathematica Scientia

基　　金：国家自然科学基金(11471290);温州大学基金(135010121413)~~

摘　　要：该文研究具时变耦合系数的非自治随机Boussinesq格点系统同时受依时间确定性外力和可加白噪声影响时的渐近行为.首先证明非自治随机Boussinesq格点方程的解生成的连续余圈的随机吸引子的存在性.然后证明此系统的随机吸引子在噪声项系数趋于零时的上半连续性.In this paper, we study the asymptomatic behavior of non-autonomous stochastic Boussinesq lattice equations with time-dependent coupled coefficients, time-dependent deterministic forces and additive white noises. Firstly, we prove the existence of a random attractor for the continuous cocycle generated by the solutions of the non-autonornous stochastic Boussinesq lattice equations. Lastly we establish the upper semi-continuity of random attractors for the random systems as the intensity of the noises tends to zero.

关 键 词：随机Boussinesq格点方程 连续余圈 随机吸引子 上半连续性 可加白噪声 

分 类 号：O193[理学—数学]