Homogenization of a singular random one-dimensional PDE

TL;DR

This paper investigates the homogenization of a one-dimensional parabolic PDE with random coefficients and a large zero order term, demonstrating convergence in law to a random limit process under appropriate scaling.

Contribution

It introduces a novel scaling approach for the zero order term in a singular PDE with random coefficients, establishing convergence to a random limit process.

Findings

Solutions converge in law under proper scaling

The limit process remains random

Provides a description of the limit dynamics

Abstract

This paper deals with the homogenization problem for a one-dimensional parabolic PDE with random stationary mixing coefficients in the presence of a large zero order term. We show that under a proper choice of the scaling factor for the said zero order terms, the family of solutions of the studied problem converges in law, and describe the limit process. It should be noted that the limit dynamics remain random.