Speaker: Guanying Peng (University of Arizona)
Title: Understanding defects in materials from a variational perspective
Abstract: Defects occur naturally in materials and physical systems, e.g., in superconductors, liquid crystals, thin film blisters, pattern formation systems. Understanding the mechanisms behind different types of defects raises interesting and challenging mathematical questions, and is important in applications. In this talk, I will discuss a variational model, called the Aviles-Giga energy, that has been used to understand defects in thin film blisters. The model allows coexistence of point and line defects in 2D. The variational analysis of this problem is a long standing open problem with difficulties coming from the associated function space. I will present some recent progress towards clarifying some of the central issues in this problem. The underlying PDE of the problem has a strong hyperbolic nature and our analysis relies on some central tools from hyperbolic conservation laws.