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An introduction to homogenization theory

Termine

Termine
Mo
10:00 - 12:00 Uhr
Vorlesung
H 3025
Dr. Martin Heida
Sekretariat
MA 568
Alexandra Schulte

Beschreibung

Homogenization theory deals with partial differential equations that have highly oscillating coefficients and / or are formulated on domains with periodic holes of small size and distance. The aim of the theory is to understand the influence of the microscopic structures onto the macroscopic behaviour of the solutions of the PDE. Example are the porous media flow, reactions and diffusion in catalyzers and chromatographs or heat transport in polycrystals. We introduce the most common methods of asymptotic expansion, two-scale convergence and unfolding and apply them to reaction-diffusion equations.

This lecture belongs to the modul "Fortgeschrittene Themen der Differentialgleichungen".

Voraussetzungen

Differential Equations I
Analysis III
preferable: Basic knowledge on Hilbert spaces, weak convergence, Banach-Alaoglu theorem, Lax-Milgram lemma

Literatur

Wird in der Vorlesung bekanntgegeben.

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