Homogenization of elliptic equations in periodic domains: The case of elliptic equations of the curl type

Abstract

In this thesis, we homogenize elliptic equations in the periodically perforated domain. The two scale convergence method is used in this work for the homogenization. In particular, we homogenize the quasilinear elliptic equation with the dirichlet boundary condition, the time independent incompressible reynolds equation as well as the elliptic equation of the curl type of which the Maxwell type equations is a typical example. We obtain the cell problems and the homogenized equations for the problems which could easily be solved using any numerical method such as matlab or comsol in place of the original problems which contain the fast oscillating parameter ".