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Strong convergence in averaging principle for stochastic hyperbolic-parabolic equations with two time-scales. (English) Zbl 1322.60111
Summary: This article deals with averaging principles 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, effective dynamics for the slow variable, which take the form of a stochastic wave equation, are derived. Also, the rate of strong convergence for the slow component towards the solution of the averaging equation is obtained as a byproduct.

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60F15 Strong limit theorems
70K70 Systems with slow and fast motions for nonlinear problems in mechanics
Full Text: DOI
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