Homogeneizazio asintotikoa eta bere aplikazioak deribatu partzialeko ekuazioen analisian

Abstract

The main objective of this article is to make a brief introduction of the theory of asymptotic homogenization and give some examples of applications that this theory may have in the study of some partial differential equations. To that end, we will introduce the reader two main concepts that are used in functional analysis. On the one hand, weak convergence in Hilbert spaces; on the other hand, the spaces of weak solutions of a given partial differential equation, and, particularly, Sobolev spaces. Due to those two concepts, we will analyze the behavior of the weak solutions of an elliptic differential equation which models the heat flux in a non-homogeneous body by means of results of homogenization theory that we will develop throughout the article.