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Hlder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.
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 L-2（D）.
出处
《四川师范大学学报（自然科学版）》
CAS
北大核心
2017年第2期143-148,共6页
Journal of Sichuan Normal University（Natural Science）
基金
四川省科技厅应用基础计划项目(2016JY0204)
四川省教育厅自然科学重点科研基金(14ZA0031)
