Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

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

Pages: 911 - 926, Volume 6, Issue 4, July 2006      doi:10.3934/dcdsb.2006.6.911

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Armen Shirikyan - Laboratoire de Mathématiques, Université de Paris-Sud XI, Bâtiment 425, 91405 Orsay Cedex, France (email)

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].

Keywords:  Ergodicity, stationary measure, complex Ginzburg-Landau equation.
Mathematics Subject Classification:  Primary: 35K55, 60J25; Secondary: 35Q60, 60H15.

Received: March 2005;      Revised: November 2005;      Available Online: April 2006.