DFG Priority Research Program 1095 on
Analysis, modeling, and simulation of multiscale problems

Research Project

Quantitative homogenization and averaging

Research director

Prof. Dr. Bernold Fiedler

Members

Dr. Karsten Matthies

Summary

Problems involving different time scales are quite common in many branches of Physics and Mathematics. The difference of the scales can be explicit due to an external forcing, or implicit due to internal properties of a system. In mathematical models different scales are manifest as rapid oscillations of coefficients in time or space variables.

Our analysis of partial differential equations with rapidly oscillating coefficients in time and/or space investigates the elimination of such oscillations by averaging or homogenization techniques. For systems of parabolic and elliptic type we aim at a quantitative comparison with the averaged or homogenized equations, in particular for quasiperiodic inhomogeneities with Diophantine frequencies.