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Averaging principle for multiscale stochastic Klein-Gordon-heat system. (English) Zbl 1436.60063
Summary: This paper investigates multiscale stochastic Klein-Gordon-heat system. We establish the well-posedness and two kinds of stochastic averaging principle for stochastic Klein-Gordon-heat system with two timescales. To be more precise, under suitable conditions, two kinds of averaging principle (the autonomous case and the nonautonomous case) are proved, and as a consequence, the multiscale stochastic Klein-Gordon-heat system can be reduced to a single stochastic Klein-Gordon equation (averaged equation) with a modified coefficient, the slow component of multiscale stochastic system toward the solution of the averaged equation in moment (the autonomous case) and in probability (the nonautonomous case).

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
70K65 Averaging of perturbations for nonlinear problems in mechanics
70K70 Systems with slow and fast motions for nonlinear problems in mechanics
37H10 Generation, random and stochastic difference and differential equations
37L55 Infinite-dimensional random dynamical systems; stochastic equations
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