Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation

Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation

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Publisher
Springer-Verlag
Copyright
Copyright © 2004 by Springer
Subject
Mathematics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-004-0802-1
Publisher site
See Article on Publisher Site

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