Article

Homogenization of Heat Equation with Large Time-dependent Random Potential

01/2014;
Source: arXiv

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