Diffusive Limit of Transport Equations in Bounded Domains
Prof. Lei Wu, Lehigh University
Abstract: In this talk, I will discuss the transition from microscopic particle models to macroscopic continuum equations, a subject at the intersection of PDE and asymptotic analysis. I will focus in particular on the diffusive limit of the neutron transport equation, which serves as a prototype for more general hydrodynamic limits of kinetic equations. It also provides a setting that captures nearly all of the fundamental difficulties associated with boundary effects. In this survey-style talk, I will review these difficulties and discuss various approaches to addressing them. I will present our work over the past decade on three types of domains: smooth convex domains, smooth non-convex domains, and, most recently, polygonal domains. After a brief introduction to the Hilbert expansion, I will focus on the formulation and well-posedness of boundary layer and wedge layer problems.
Tea and refreshments available from 3:00-3:25 p.m. in the Assmus Conference Room (CU 212).
