Homogenization of Parabolic Equations with Large Time-dependent Random Potential

2014/01/16 by Yu Gu, Gu, Yu, Guillaume Bal +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1401.3806

openalex publication_date 2014/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper concerns the homogenization problem of a parabolic equation with large, time-dependent, random potentials in high dimensions d≥ 3. Depending on the competition between temporal and spatial mixing of the randomness, the homogenization procedure turns to be different. We characterize the difference by proving the corresponding weak convergence of Brownian motion in random scenery. When the potential depends on the spatial variable macroscopically, we prove a convergence to SPDE.

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