The homogenization problem of a class of stochastic partial differential equations is studied,∂tyε(t,x)=△yε(t,x)/2+Vε(x)Ayε(t,x),where d＞2,(t,x)∈(0,T)×(R)d.Here yε(t,x)=(uε(t,x),wε(t,x))T,Vε(x)is a Gaussian process with scale,in the case that its correlation function satisfies certain integrability conditions,Duhamel(iterative)expansion and Wick's theorem can be used to give the homogenizing convergence of the above equation.
关键词
Duhamel展开/Wick定理/均匀化理论/高斯过程
Key words
Duhamel expansion/Wick's theorem/homogenization theory/Gaussian process
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