Graduate Analysis Seminar
Trevor Leslie
UIC
Homogenization for Elliptic PDEs via Two-Scale Convergence
Abstract: We study the elliptic PDE $-\nabla \cdot (A^\varepsilon \nabla u^\varepsilon) = f$
on a bounded domain with Dirichlet boundary conditions, where $A^\varepsilon(x) = A(x/\varepsilon)$
and $A(y)$ is a periodic matrix with bounded coefficients. We derive an
approximation of this equation of the form $-\nabla \cdot (\overline{A} \nabla u) = f$
and prove that the solution $u$ approximates the solution $u^\varepsilon$ of the
original equation. The proof uses the method of two-scale convergence; basic properties
of two-scale convergence will be stated (without proof) for completeness.
Monday March 7, 2016 at 2:00 PM in SEO 612