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 出版日期:2018-10-26 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);温州大学基金(135010121413)

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

Min Zhao^1,*(),Shengfan Zhou²

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 Online:2018-10-26 Published:2018-11-09
Contact: Min Zhao E-mail:zhaomin1223@126.com
Supported by:
the NSFC(11471290);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.

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

参考文献 7

1	Jia Y , Zhang X , Dong B . Remarks on the blow-up criterion for smooth solutions of the Boussinesq equations with zero diffusion. Commun Pure Appl Anal, 2013, 12 (2): 923- 937
2	Wu G , Zheng X . Global well-posedness for the two-dimensional nonlinear Boussinesq equations with vertical dissipation. J Differential Equations, 2013, 255 (9): 2891- 2926 doi: 10.1016/j.jde.2013.07.023
3	Yang X , Fan Z , Li K . Uniform attractor for non-autonomous Boussinesq-type equation with critical nonlinearity. Math Method Appl Sci, 2016, 39 (11): 3075- 3087 doi: 10.1002/mma.v39.11
4	Yang Z . Longtime dynamics of the damped Boussinesq equation. J Math Anal Appl, 2013, 399 (1): 180- 190 doi: 10.1016/j.jmaa.2012.09.042
5	Zhao L , Yang M , Zhang C . Dynamics for the damped Boussinesq equation with delay. Stoch Dynam, 2016, 16 (6): 1650021 doi: 10.1142/S0219493716500210
6	耿范, 李瑞斋, 葛翔宇. 具阻尼项的Boussinesq型方程的长时间行为. 数学物理学报, 2016, 36A (6): 1196- 1210 doi: 10.3969/j.issn.1003-3998.2016.06.017
	Geng F , Li R , Ge X . Long time behavior of Boussinesq type equation with damping term. Acta Math Sci, 2016, 36A (6): 1196- 1210 doi: 10.3969/j.issn.1003-3998.2016.06.017
7	Abdallah A . Global attractor for the lattice dynamical system of a nonlinear Boussinesq equation. Abstr Appl Anal, 2005, 6: 655- 671

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