Homogenization, oscillation and randomness in PDE and FBP,
7.5 course credit, Spring 2008. 

URL: http://www.math.kth.se/~henriksh/

 

Course Leader:

Henrik Shahgholian , 08-790 6754, henriksh@math.kth.se
Start:  Monday February 4,   13.15-15.00, at room 3733, Building of the  Dept. of Mathematics.

This course is partly self-studying. The lectures will take place Mondays:

February 4,11, 18, 25,       March 3, 17, 24,            April 7,             Students presentations: May 5, 12, 19, 26.

There will be a break of 3 weeks and during this period the students  will pick up a certain material for presentation (1h).

See  SCHEDULE

Language: English.

Goal

To learn about certain problems in classical homogenization and oscillation (hopefully something about random media). The core application will be towards free boundary problems.

Topics

Basic tools: L^p spaces, (weak) convergences, periodic functions, Sobolev spaces,

Basic PDE: Existence theory, viscosity solutions, variational formulation,

Basic FBP: Obstacle problem, weak and variational form, Flame propagations,

Physical models in homogenization,

Methods of homogenizations: Multi-scale method, oscilating test function, two-scale method, correctors,

 Periodic, non-periodic, and random homogenization (articles)

Prerequisites

Contact the course leader. In general you need some background in functional analysis, and introductory pde. The course is open to both advanced undergraduate and graduate students.

Literature

An introduction to homogenization, by Doina Cioranescu & Patrizia Donato;

published papers.

Examination

 The examination will consist of