Homogenization of Parabolic Equations with Large Time-dependent Random Potential

Abstract

This paper concerns the homogenization problem of a parabolic equation with large, time-dependent, random potentials in high dimensions $d\ge 3$. 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.

23 pages, to appear in SPA

References in corpus (4)

• Homogenization of a singular random one-dimensional PDE
• Random homogenisation of a highly oscillatory singular potential
• Weak Convergence Approach for Parabolic Equations with Large, Highly Oscillatory, Random Potential
• Kantorovich distance in the martingale CLT and quantitative homogenization of parabolic equations with random coefficients