Light PhD Seminar: Asymptotic homogenization and its applications in the analysis of partial differential equations

The purpose of this talk is to introduce the mathematical theory of asymptotic homogenization. Homogenization, which is a method of studying partial differential equations with rapidly oscillating coefficients, describes the macroscopic properties of a composite material by taking into account properties of the microscopic structure. Particularly, we are going to see the base results of this field. Likewise, we are going to analyze the behavior of the weak solutions of an elliptic equation which models the heat flux in a non-homogeneous body by means of theoretical results of homogenization theory that we will develop throughout the talk.