Inertial manifolds and forms for stochastically perturbed retarded semilinear parabolic equations

被引：2

作者：

Chueshov I.D. ^{[1
]}

Scheutzow M. ^{[2
]}

机构：

[1] Department of Mechanics and Mathematics, Kharkov University, 310077 Kharkov

[2] Fachbereich 3, MA 7-5, Technische Universität Berlin, D-10623 Berlin

来源：

Journal of Dynamics and Differential Equations | 2001年 / 13卷 / 2期

关键词：

Attractor; Inertial manifold and form; Invariant measure; Perfect cocycle; Stochastic PDE with delay;

D O I：

10.1023/A:1016684108862

中图分类号：

学科分类号：

摘要：

We construct inertial manifolds for a class of random dynamical systems generated by retarded semilinear parabolic equations subjected to additive white noise. These inertial manifolds are finite-dimensional invariant surfaces, which attract exponentially all trajectories. We study the corresponding inertial forms, i.e., the restriction of the stochastic equation to the inertial manifold. These inertial forms are finite-dimensional Ito equations and they completely describe the long-time dynamics of the system under consideration. The existence of inertial manifolds and the properties of inertial forms allow us to show that under mild additional conditions the system has a global (random) attractor in the sense of the theory of random dynamical systems. © 2001 Plenum Publishing Corporation.

引用

页码：355 / 380

页数：25

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