四川师范大学学报（自然科学版）2017，Vol.40Issue(2)：143-148,6.DOI:10.3969/j.issn.1001-8395.2017.02.001
带乘性噪声的广义2D Ginzburg-Landau方程的渐近行为
The Asymptotic Behavior of the Generalized 2D Ginzburg-Landau Equation with Multiplicative Noise
摘要
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).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Key words
Generalized 2D Ginzburg-Landau equation/random dynamical systems/random attractor/multiplicative noise分类
数理科学引用本文复制引用
杨袁,舒级,王云肖,李倩,汪春江..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）,2017,40(2):143-148,6.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) （2016JY0204）
