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

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.