Strong convergence in averaging principle for stochastic hyperbolic-parabolic equations with two time-scales

This article deals with averaging principle for stochastic hyperbolic-parabolic equations with slow and fast time-scales. Under suitable conditions, the existence of an averaging equation eliminating the fast variable for this coupled system is proved. As a consequence, an effective dynamics for slow variable which takes the form of stochastic wave equation is derived. Also, the rate of strong convergence for the slow component towards the solution of the averaging equation is obtained as a byproduct.