Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation |
| |
Authors: | Tomás Caraballo Peter E Kloeden and Björn Schmalfuß |
| |
Institution: | (1) Departamento Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain;(2) Fachbereich Mathematik, Johann Wolfgang Goethe-Universität, D-60054 Frankfurt am Main, Germany;(3) Fakultät 5 – Mathematik, Universität Paderborn, D-33095 Paderborn, Germany |
| |
Abstract: | We consider the exponential stability of stochastic evolution
equations with Lipschitz continuous non-linearities when zero is
not a solution for these equations. We prove the existence of a
non-trivial stationary solution which is exponentially stable,
where the stationary solution is generated by the composition of a
random variable and the Wiener shift. We also construct stationary
solutions with the stronger property of attracting bounded sets
uniformly. The existence of these stationary solutions follows
from the theory of random dynamical systems and their attractors.
In addition, we prove some perturbation results and formulate
conditions for the existence of stationary solutions for
semilinear stochastic partial differential equations with
Lipschitz continuous non-linearities. |
| |
Keywords: | Random dynamical systems Stationary
solutions Exponential stability Stabilization |
本文献已被 SpringerLink 等数据库收录! |
|