Speaker: Erik Grandelius (UiO)
Title: Homogenization of PDEs
Abstract: Highly heterogeneous media gives rise to PDEs with complicated oscillatory microscopic structure. Homogenization theory is an attempt at capturing essential macroscopic features of the medium with a simplified averaged model. A fundamental mathematical problem when deriving the averaged model is the incompatibility of weak convergence with nonlinear operations. In this seminar we discuss the classical elliptic homogenization problem, parabolic equations on oscillating surfaces and homogenization of conservation laws. One application is the cardiac bidomain model, where the cellular structure provides the underlying heterogeneity.