Homogenization of linear and semilinear second order parabolic PDEs with periodic coefficients: A probabilistic approach. (English) Zbl 0935.35010

Second-order parabolic linear and semilinear equations are considered with rapidly oscillating periodic coefficients. The solutions are proved to converge to solutions of a limiting equation with constant coefficients being the averages in some sense of the corresponding coefficients of the original equation. The methods of proofs are of probabilistic nature. For the linear equation the Feynman-Kac formula is used, and for the semilinear equations the solutions are represented by means of backward stochastic differential equations.


35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
60H30 Applications of stochastic analysis (to PDEs, etc.)
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