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...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2004 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/23668 |
| Acceso en línea: | http://hdl.handle.net/11441/23668 https://doi.org/10.1007%2Fs00245-004-0802-1 |
| Access Level: | acceso abierto |
| Palabra clave: | Random dynamical systems stationary solutions exponential stability stabilization |
| Sumario: | 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 semi-linear stochastic partial differential equations with Lipschitz continuous non-linearities. |
|---|