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Introduction to the homogenization theory (Winter Semester 2013/14)

In many problems of physics and mechanics processes in media with rapidly oscillating spatial local characteristics are studied. There are two main types of such media:

- composite materials in which the physical processes are described by PDEs with highly oscillating (with respect to spatial variables) coefficients;

- strongly perforated media in which the physical processes are described by boundary value problems in domains with complicated geometry.

It is practically impossible to solve these problems either by analytical or numerical methods. However when the scale of the microstructure of the medium is much smaller than the scale of the physical process under consideration, the medium has homogenized characteristics (which, in general, differs from local ones). The problem of the homogenization theory is to find these characteristics and using them to construct the homogenized model approximating the initial one and giving global description of the physical process in microinhomogeneous media.

The course devoted to some basic problems and methods of the homogenization theory.

More information about the course (plan, literature, requirements) you can find on my personal page.

Lecture: Tuesday 8:00-9:30 1C-01 Begin: 22.10.2013
Lecturer PD Dr. Andrii Khrabustovskyi
Office hours: by appointment
Room 3.037 Kollegiengebäude Mathematik (20.30)
Email: andrii.khrabustovskyi@kit.edu