带可加噪声的非自治随机Boussinesq格点方程的随机吸引子

数学物理学报 ›› 2018, Vol. 38 ›› Issue (5): 924-940.

带可加噪声的非自治随机Boussinesq格点方程的随机吸引子

赵敏¹, 周盛凡²

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

收稿日期:2017-02-13 修回日期:2017-11-11 出版日期:2018-11-09 发布日期:2018-11-09
通讯作者: 赵敏 E-mail:zhaomin1223@126.com
基金资助:
国家自然科学基金（11471290）和温州大学基金（135010121413）

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

Zhao Min¹, Zhou Shengfan²

1 College of Mathematics, Physics and Electronic Information Engineering, Wenzhou University, Zhejiang Wenzhou 325035;
2 College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Zhejiang Jinhua 321004

Received:2017-02-13 Revised:2017-11-11 Online:2018-11-09 Published:2018-11-09
Supported by:
Supported by the NSFC(11471290) and the Foundation of Wenzhou University (135010121413)

摘要/Abstract

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.

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

Abstract: 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-autonomous 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.

Key words: Stochastic Boussinesq lattice equations, Continuous cocycle, Random attractor, Upper semi-continuity, Additive white noise

中图分类号:

O193

赵敏, 周盛凡. 带可加噪声的非自治随机Boussinesq格点方程的随机吸引子[J]. 数学物理学报, 2018, 38(5): 924-940.

Zhao Min, Zhou Shengfan. Random Attractor for Non-Autonomous Stochastic Boussinesq Lattice Equations with Additive White Noises[J]. Acta mathematica scientia,Series A, 2018, 38(5): 924-940.

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