Homogenization of semilinear parabolic PDEs with the third boundary conditions

TL;DR

This paper develops a probabilistic approach to homogenize semilinear parabolic PDEs with third boundary conditions and oscillating coefficients, utilizing backward stochastic differential equations with singular coefficients.

Contribution

It introduces a novel probabilistic method for homogenization of third boundary value problems in semilinear parabolic PDEs, extending previous work with new stochastic techniques.

Findings

Effective homogenization method for PDEs with third boundary conditions

Use of backward stochastic differential equations with singular coefficients

Framework applicable to periodic oscillating coefficients

Abstract

In this paper, we study the homogenization of the third boundary value problem for semilinear parabolic PDEs with rapidly oscillating periodic coefficients in the weak sense. Our method is entirely probabilistic, and builds upon the work of [28] and [3]. Backward stochastic differential equations with singular coefficients play an important role in our approach.