LAUSR

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).