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Exponential mixing for a stochastic partial differential equation driven by degenerate noise. (English) Zbl 0992.60067

Summary: We study stochastic partial differential equations of the reaction-diffusion type. We show that, even if the forcing is highly degenerate (i.e. does not have full rank), there is exponential convergence towards the invariant measure. The convergence takes place in the topology induced by a weighted variation norm and uses a kind of (uniform) Doeblin condition.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
37L99 Infinite-dimensional dissipative dynamical systems
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