Homogenization of linear and semilinear second order parabolic PDEs with periodic coefficients: A probabilistic approach
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.
rapidly oscillating periodic coefficients
scientific article; zbMATH DE number 1367856
scientific article