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Polynomial mixing for the complex Ginzburg-Landau equation perturbed by a random force at random times. (English) Zbl 1145.35323
Summary: In this paper we study the problem of ergodicity for the complex Ginzburg-Landau (CGL) equation perturbed by an unbounded random kick-force. Randomness is introduced both through the kicks and through the times between the kicks. We show that the Markov process associated with the equation in question possesses a unique stationary distribution and satisfies a property of polynomial mixing.

MSC:
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35K55 Nonlinear parabolic equations
60J25 Continuous-time Markov processes on general state spaces
35R60 PDEs with randomness, stochastic partial differential equations
35Q55 NLS equations (nonlinear Schrödinger equations)
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