Course: STAT 31260=CAAM 31260
Title: Homogenization of Partial Differential Equations
Instructor: Thuyen Dang
Class Schedule: Sec 1: TR 12:30 PM–1:50 PM in TBA
Description: This course introduces common methods for establishing the macroscopic behavior of heterogeneous differential equations. It begins with a brief review of some classical results in functional analysis (weak/weak-* convergence and Sobolev spaces), followed by a discussion of several toolboxes: formal asymptotic expansion, compensated compactness, two-scale convergence, and Gamma-convergence. Along the way, the course presents surprising phenomena that have appeared in homogenization, such as strange terms, negative Poisson ratios, and nonlocal terms. If time permits, large-scale regularity by the compactness method will also be discussed.