Homogenization of Partial Differential Equations

In this lecture we are interested in partial differential equations and variational models that feature multiple length scales, randomness, and nonlinearities. Although mathematical modelling is not the focus of this lecture, let me mention that multiscale models  often appear in mechanical models of materials that feature mircorstructure, e.g. composite materials, polycrystalls, bone. 
In the lecture we focus on homogenization theory,  which is about rigorously passing from models with one or more small scales to a macroscopic, effective description. In the first part of the lecture we study homogenization of linear elliptic PDEs with periodic and random coefficients. We then advance to nonlinear problems and quantitative properties.

The lecture will be partially based on a lecture series that I presented at the GSIS International Winter School 2017 at Tohoku University, Japan.

Target group: Master students (mathematics, physics) and Phd-students, young postdocs

Prerequisites:

• Basic concepts from PDE theory (e.g. weak solutions, Sobolev spaces)
• Basic concepts from functional analysis (e.g. Lax-Milgram, weak topology)
• Basic concepts from probability theory (e.g. measure theory, law of large numbers)

Format:

The lecture will be taught remotely (or in hybrid form)  following the flipped classroom concept.

Further information is available after registration.