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Tuesday, February 6, 2018

**Abstract:** This talk introduce some effective modelling for some SPDEs with separated time scales. First we consider SPDEs with slow-fast part and averaging method is applied to derive the averaged approximation model. Normal deviation is also considered and large deviations further confirms the effectivity of the averaged equation plus the normal deviation. Second, we consider diffusion approximation for a Burgers type equation wit stochastic advection. By constructing a martingale, the approximation on both finite tie interval and infinite time interval is derived. Last the diffusion approximation is also applied to study the Smoluchowski-Kramers approximation for a nonlinear wave equation with state-dependent damping and random fluctuation.