[1]王云肖,舒 级*,杨 袁,等.加权空间中带乘性噪声的随机分数阶非自治Ginzburg-Landau方程[J].四川师范大学学报(自然科学版),2019,42(04):491-500.[doi:10.3969/j.issn.1001-8395.2019.04.009]
 WANG Yunxiao,SHU Ji,YANG Yuan,et al.Stochastic Fractional Non-autonomous Ginzburg-Landau Equations with Multiplicative Noise in Weighted Space[J].Journal of SichuanNormal University,2019,42(04):491-500.[doi:10.3969/j.issn.1001-8395.2019.04.009]
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加权空间中带乘性噪声的随机分数阶非自治Ginzburg-Landau方程()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
42卷
期数:
2019年04期
页码:
491-500
栏目:
基础理论
出版日期:
2019-06-15

文章信息/Info

Title:
Stochastic Fractional Non-autonomous Ginzburg-Landau Equations with Multiplicative Noise in Weighted Space
文章编号:
1001-8395(2019)04-0491-10
作者:
王云肖 舒 级* 杨 袁 李 倩 汪春江
四川师范大学 数学科学学院, 四川 成都 610066
Author(s):
WANG Yunxiao SHU Ji YANG Yuan LI Qian WANG Chunjiang
College of Mathematics Science, Sichuan Normal University, Chengdu 610066, Sichuan
关键词:
随机分数阶Ginzburg-Landau方程 随机动力系统 随机吸引子 乘性噪声 加权空间
Keywords:
stochastic fractional Ginzburg-Landau equation random dynamical system random attractor multiplicative noise weighted space
分类号:
O175.2
DOI:
10.3969/j.issn.1001-8395.2019.04.009
文献标志码:
A
摘要:
考虑带乘性噪声的随机分数阶非自治Ginzburg-Landau方程在加权空间L2ρ(Rn)中的渐近性质.首先将随机偏微分方程转化为仅含随机参数的随机方程,然后对该方程的解进行先验估计,并通过尾估计得到渐近紧性成立,从而随机动力系统的紧性成立,最后证明L2ρ(Rn) 中随机吸引子的存在性.
Abstract:
In this paper, we consider the asymptotic dynamic for Random attractors of stochastic fractional non-autonomous Ginzburg-Landau equations with multiplicative noise in L2ρ(Rn ). In the first, we transform the partial differential equation into the random equation that only indudes the random parameters. Then, using estimates for far-field values of solutions and a cut-off technique, asymptotic compactness is proved. At last, the existence of a random attractor in L2ρ(Rn) for the random dynamical system is established.

参考文献/References:

[1] CRAUEL H, FLANDOLI F. Attractors for random dynamical systems[J]. Probability Theory and Related Fields,1994,100(3):365-393.
[2] CRAUEL H, DEBUSSCHE A, FLANDOLI F. Random attractors[J]. J Dynamics and Differential Equations,1997,9(2):307-341.
[3] ARONLD L. Random Dynamical Systems[M]. New York:Springer-Verlag,1998.
[4] DOERING C R, GIBBON J D, HOLM D, et al. Low-dimensional behavior in the complex Ginzburg-Landau equation[J]. Nonlinearity,1988,1(2):279-309.
[5] GHIDAGLIA J M, HÉRON B. Dimension of the attractor associated to the Ginzburg-Landau equation[J]. Physica D:Nonlinear Phenomena,1987,28(3):282-304.
[6] BARTUCCELLI M, CONSTANTIN P, DOERING C R, et al. On the possibility of soft and hard turbulence in thecomplex Ginzburg-Landau equation[J]. Physica D:Nonlinear Phenomena,1990,44(3):421-444.
[7] DOERING C R, GIBBON J D, LEVERMORE C D. Weak and strong solutions of the complex Ginzburg-Landau equation[J]. Physica D:Nonlinear Phenomena,1994,71(3):285-318.
[8] LEVERMORE C D, OLIVER M. The complex Ginzburg-Landau equation as a model problem[C]//Lectures in Applied Mathematics. Providence:American Mathematical Society,1997.
[9] BATUCCELLI M, GIBBON J D, OLIVER M. Lengths scales in solutions of the complex Ginzburg-Landau equation[J]. Physica D:Nonlinear Phenomena,1996,89(3):267-286.
[10] LI D L, GUO B L. On Cauchy problem for generalized complex Ginzburg-Landau equation in three dimensions[J]. Progress in Natural Science,2003,13(9):658-665.
[11] LI D L, DAI Z D. Long time behavior of solution for generalized Ginzburg-Landau equation[J]. J Math Anal Appl,2007,330(2):934-948.
[12] GUO B L, WANG X. Finite dimensional behavior for the derivative Ginzburg-Landau equation in two spatial dimensions[J]. Physica D:Nonlinear Phenomen,1995,89(1):83-99.
[13] PU X K, GUO B L. Well-posedness and dynamics for the fractional Ginzburg-Landau equation[J]. Applicable Analysis,2013,92(2):318-334.
[14] 李栋龙,郭柏灵. 带附加噪声的随机广义 2D Ginzburg-Landau 方程的渐进行为[J]. 应用数学和力学,2009,30(8):883-894.
[15] LU H, LÜ S J. Random attractor for fractional Ginzburg-Landau equation with multiplicative noise[J]. Taiwanese J Mathematics,2014,18(2):435-450.
[16] HUANG J H, SHEN T L. Dynamics of stochastic fractional boussinesq equations[J]. Discrete and Continuous Dynamical Systems,2015,B20:2051-2067.
[17] 张佳,舒级,董建,等. 具乘性噪声的广义Ginzburg-Landau方程的随机吸引子[J]. 四川师范大学学报(自然科学版),2015,38(5):638-643.
[18] 鲍杰,舒级. 高阶广义2D Ginzburg-Landau方程的随机吸引子[J]. 四川师范大学学报(自然科学版),2014,37(3):298-306.
[19] LU H, BATES P W, XIN J, et al. Asymptotic behavior of stochastic fractional power dissipative equations on Rn[J]. Nonlinear Analysis:TMA,2015,128:176-198.
[20] LU H, BATES P W, LÜ S, ZHANG M. Dynamics of the 3D fractional Ginzburg-Landau equation with multi0plicative noise on an unbounded domain[J]. Communications in Mathematical Sciences,2016,14(1):273-295.
[21] ZHOU S, ZHAO M. Random attractors for damped non-autonomous wave equations with memory and white noise[J]. Nonlinear Analysis:TMA,2015,120:202-226.
[22] 贾秋丽,周盛凡. 加权空间一阶耗散格点动力系统的吸引子[J]. 河南科技大学学报(自然科学版),2012,33(4):69-74.
[23] BATES P W, LU K N, WANG B X. Tempered random attractors for parabolic equations in weighted spaces[J]. J Mathematical Physics,2013,54(8):221-243.

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备注/Memo

备注/Memo:
收稿日期:2017-07-16 接受日期:2017-11-20
基金项目:国家自然科学基金(11371267和11571245)和四川省科技厅应用基础项目(2016JY0204)
*通信作者简介:舒 级(1976—),男,教授,主要从事随机动力系统、偏微分方程的研究,E-mail:shuji2008@hotmail.com
更新日期/Last Update: 2019-06-15