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July  2006, 6(4): 911-926. doi: 10.3934/dcdsb.2006.6.911

Ergodicity for a class of Markov processes and applications to randomly forced PDE'S. II

Armen Shirikyan 1,

1. 

Laboratoire de Mathématiques, Université de Paris-Sud XI, Bâtiment 425, 91405 Orsay Cedex

Received  March 2005 Revised  November 2005 Published  April 2006

The paper is devoted to studying the problem of ergodicity for the complex Ginzburg--Landau (CGL) equation perturbed by an external random force. We show that the conditions of a simple general result established in [22] are fulfilled for the equation in question. As a consequence, we prove that the corresponding family of Markov processes has a unique stationary distribution, which possesses a mixing property. The result of this paper was announced in the joint work with Sergei Kuksin [14].
Keywords: complex Ginzburg-Landau equation., Ergodicity, stationary measure.
Mathematics Subject Classification: Primary: 35K55, 60J25; Secondary: 35Q60, 60H1.
Citation: Armen Shirikyan. Ergodicity for a class of Markov processes and applications to randomly forced PDE'S. II. Discrete and Continuous Dynamical Systems - B, 2006, 6 (4) : 911-926. doi: 10.3934/dcdsb.2006.6.911
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