The Burgers equation with affine linear noise: Dynamics and stability

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Mohammed, Salah¹  Zhang, Tusheng² 

[1] So Illinois Univ, Dept Math, Carbondale, IL 62901 USA

[2] Univ Manchester, Dept Math, Manchester M13 9PL, Lancs, England

关键词: Burgers equation;    Affine linear noise;    Perfect cocycle;    Multiplicative ergodic theory;    Lyapunov spectrum;    Stationary solution;    Hyperbolicity;    Local stable manifold theorem;    Invariant manifolds;    Global invariant foliation;   

DOI  :  10.1016/j.spa.2011.12.002

来源: Elsevier

【 摘 要 】

We study the dynamics of the Burgers equation on the unit interval driven by affine linear noise. Mild solutions of the Burgers stochastic partial differential equation generate a smooth perfect and locally compacting cocycle on the energy space. Using multiplicative ergodic theory techniques, we establish the existence of a discrete non-random Lyapunov spectrum for the cocycle. We establish a local stable manifold theorem near a hyperbolic stationary point, as well as the existence of local smooth invariant manifolds with finite codimension and a countable global invariant foliation of the energy space relative to an ergodic stationary point. (c) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free