Homogenization of Semilinear Parabolic PDEs with the Third Boundary Conditions

Abstract

In this paper, the authors study the homogenization of the third boundary value problem for semilinear parabolic PDEs with rapidly oscillating periodic coefficients in the weak sense. Their method is entirely probabilistic, and builds upon the work of Tanaka (2020) and Buckdahn (1999). Backward stochastic differential equations with singular coefficients play an important role in this approach.

Keywords

Homogenization / Weak solution / Third boundary value problem / Backward stochastic differential equations / 60H30 / 35B27 / 35K40

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