一类随机波动方程的随机吸引子的维数估计  

On Hausdorff Dimension of Random Attractors for a Stochastic Wave Equation

作　　者：班爱玲[1] BAN Ai-ling(College of Mathematics and Computer,Chizhou College,Chizhou 247000)

机构地区：[1]池州学院数学与计算机学院

出　　处：《湖南师范大学自然科学学报》2019年第6期72-76,共5页Journal of Natural Science of Hunan Normal University

基　　金：安徽省自然科学基金青年项目(1708085QA13);池州学院自然科学基金(2016ZRZ009)

摘　　要：本文主要研究具有临界增长指数的强阻尼随机波动方程的随机吸引子的Hausdorff维数的上界估计,并证明该随机吸引子的Hausdorff维数的上界随强阻尼系数的增大而变小,当强阻尼系数充分大时,它的Hausdorff维数是一致有界的。This paper mainly examines the upper bound estimation of the Hausdorff dimension of random attractors for strongly damped stochastic wave equations with critical growth exponents.We prove that the obtained upper bound of the Hausdorff dimension of random attractor deceases as the strongly damped coefficient grows and is uniformly bounded when the strongly damped coefficient is sufficiently large.

关 键 词：强阻尼 波动方程 随机吸引子 HAUSDORFF维数 

分 类 号：O175.2[理学—数学]