陈章,李玲玉.带有随机初值的复值Ginzburg-Landau方程的弱平均动力学*[J].数学年刊A辑,2022,43(4):415~430
带有随机初值的复值Ginzburg-Landau方程的弱平均动力学*
Weak Mean Dynamics for Complex Ginzburg-Landau Equations with Random Initial Data
Received:March 27, 2021  Revised:October 22, 2022
DOI:10.16205/j.cnki.cama.2022.0027
中文关键词:  复值Ginzburg-Landau方程, 随机初值, 平均随机动力系统, 弱拉回平均吸引子, 加权空间
英文关键词:Complex Ginzburg-Landau equation, Random initial data, Mean random dynamical system, Weak pullback mean attractor, Weighted space
基金项目:国家自然科学基金(No.11471190, No.11971260)
Author NameAffiliation
CHEN Zhang School of Mathematics, Shandong University, Jinan 250100, China. 
LI Lingyu Corresponding author. School of Mathematics, Shandong University, Jinan 250100, China. 
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中文摘要:
      本文研究了无界域上的带有随机初值的复值Ginzburg-Landau方程.首先, 基于解过程的全局适定性, 建立了带有随机初值的Ginzburg-Landau方程的平均随机动力系统.然后, 证明了弱拉回平均随机吸引子的存在唯一性以及随机吸引子的周期性,并将其进一步推广到加权空间L2(?, L2σ(R)).
英文摘要:
      In this paper, complex-valued Ginzburg-Landau equations with random initial data on unbounded domains are investigated. First, based on the global well-posedness of solution processes, the mean random dynamical system associated with such equation with random initial data is established. Then, the existence and uniqueness of weak pullback mean random attractors are proved, as well as the periodicity of random attractors, which are further extended to a weighted space L2(?, L2σ(R)).
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