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

Armen Shirikyan

doi:10.3934/dcdsb.2006.6.911

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2006, Volume 6, Issue 4: 911-926. Doi: 10.3934/dcdsb.2006.6.911

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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: February 28, 2005

Revised: October 31, 2005

Published: June 2006

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Abstract

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].

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Mathematics Subject Classification: Primary: 35K55, 60J25; Secondary: 35Q60, 60H15.

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