Applied Math Seminar

Date: Friday September 16

Time: 11:00am-11:50am

Location: GP 346

Speaker: Shibin Dai (Department of Mathematics, The University of Alabama)

Title: Degenerate diffusion and interface motion of single layer and bilayer structures

Abstract: Degenerate diffusion plays an important role in the interface motion of complex structures. The degenerate Cahn-Hilliard equation is a widely used model for single layer structures. It has been commonly believed that degenerate diffusion eliminates diffusion in the bulk phases and results in surface diffusion only. We will show that due to the curvature effect there is porous medium diffusion in the bulk phases, and the geometric evolution of single layer structures is mediated by the porous medium diffusion process. We will also discuss the existence of weak solutions for the degenerate CH equation. For bilayer structures the Functionalized Cahn-Hilliard (FCH) equation is a new model that has been extensively studied in recent years. We will discuss the existence and nonnegativity of weak solutions for the degenerate FCH equation, and the corresponding interface motions.