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Homogenization for stochastic reaction-diffusion equations with singular perturbation term

The second author is supported by NSFC Grant No. 11531006 and Science Climbing Program of Southeast University

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  • The main purpose of this paper is to study the homogenization problem of stochastic reaction-diffusion equations with singular perturbation term. The difficulty in studying such problems is how to get the uniform estimates of the equations under the influence of the singularity term. Firstly, we use the properties of the elliptic equation corresponding to the generator to eliminate the influence of singular terms and obtain the uniform estimates of the slow equation and thus, get the tightness. Finally, we prove that under appropriate assumptions, the slow equation converges to a homogenization equation in law.

    Mathematics Subject Classification: Primary: 60H15, 70K70; Secondary: 37A25.

    Citation:

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