Homogenization of Parabolic Partial Differential Equation Using the Multiple-Scale Expansion Method

Abstract

In this thesis, we have homogenization of parabolic partial differential equation using the multiple scale expansion method as its central axis. It consists of two introductory chapters into the theory of homogenization, a section is devoted to preliminary concepts and ideas needed to understand the core content of this work. We also highlighted on how the multiple scale expansion technique can be used in homogenizing elliptic partial differential equations. Finally, homogenization of parabolic partial differential equation using the multiple scale expansion method which is the focal point of this work was investigated and the results presented. The rapidly oscillating coefficient of the parabolic partial differential equation is replaced by a constant known as the homogenized coefficient.