[1]杨 袁,舒 级*,王云肖,等.带乘性噪声的广义2D Ginzburg-Landau方程的渐近行为[J].四川师范大学学报(自然科学版),2017,(02):143-148.[doi:10.3969/j.issn.1001-8395.2017.02.001]
 YANG Yuan,SHU Ji,WANG Yunxiao,et al.The Asymptotic Behavior of the Generalized 2D Ginzburg-Landau Equation with Multiplicative Noise[J].Journal of SichuanNormal University,2017,(02):143-148.[doi:10.3969/j.issn.1001-8395.2017.02.001]
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带乘性噪声的广义2D Ginzburg-Landau方程的渐近行为()
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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:
期数:
2017年02期
页码:
143-148
栏目:
基础理论
出版日期:
2017-02-01

文章信息/Info

Title:
The Asymptotic Behavior of the Generalized 2D Ginzburg-Landau Equation with Multiplicative Noise
文章编号:
1001-8395(2017)02-0143-06
作者:
杨 袁 舒 级* 王云肖 李 倩 汪春江
四川师范大学 数学与软件科学学院, 四川 成都 610066
Author(s):
YANG Yuan SHU Ji WANG Yunxiao LI Qian WANG Chunjiang
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan
关键词:
随机广义2D Ginzburg-Landau方程 随机动力系统 随机吸引子 乘性噪声
Keywords:
Generalized 2D Ginzburg-Landau equation random dynamical systems random attractor multiplicative noise
分类号:
O177.92
DOI:
10.3969/j.issn.1001-8395.2017.02.001
文献标志码:
A
摘要:
复Ginzburg-Landau方程是非线性科学中的重要模型,在物理学中的各个不同的分支都起着重要的作用.讨论一类具乘性噪声的随机广义2D Ginzburg-Landau方程的渐近行为,在Grauel H. 和Flandoli F.(Probability Theory and Related Fields,1994,100:365-393.)建立的理论基础上,运用先验估计的方法加以证明.首先对方程的乘性噪声项进行预处理,然后运用Hölder和Young不等式以及Gronwall引理给出方程在H和V中的吸收集的存在性,从而证明该方程所对应的随机动力系统在L2中随机吸引子的存在性.
Abstract:
Complex Ginzburg-Landau equation, an important model in nonlinear science, plays a fundamental role in various branches of physics. In this paper, we consider the asymptotic behavior for genenralized 2D Ginzburg-Landau equation with multiplicative noise. The result is verified with a priori estimate which is based on the theory established by Crauel and Flandoli(Probability Theory and Related Fields,1994,100:365-393.). At first, we preprocess the multiplicative nosie terms. And then, with the Holder and Young inequalities and Gronwall Lemma, we obtain the existence of abstracting set when equations are in H and V. As a consequence, we prove the existence of random attractor of random dynamical system associated with the equation in L2(D).

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备注/Memo

备注/Memo:
基金项目:四川省科技厅应用基础计划项目(2016JY0204)和四川省教育厅自然科学重点科研基金(14ZA0031)
*通信作者简介:舒 级(1977—),男,副教授,主要从事随机动力系统和偏微分方程的研究,E-mail:shuji2008@hotmail.com
更新日期/Last Update: 2017-02-01