AWM: "Partial Differential Equations: Calculus (and more!) at work"

Donatella Danielli-Garofalo, Purdue University
Abstract: From the 18th century onward, huge strides were made in the application of mathematical ideas to problems arising in the physical sciences such as heat propagation, sound and light diffusion, fluid dynamics, elasticity, electricity, and magnetism, just to name a few. The interplay between the mathematical theory and its applications led to many new fundamental discoveries in both. One of the main unifying themes is the notion of a partial differential equation (PDE), which is a relation satisfied by an unknown function of several variables and its partial derivatives. Remarkably, very different phenomena can be modeled by the same PDE (or system of PDEs). In this talk we will give a brief historical account of the evolution of the theory of PDEs, and highlight some of the fundamental results of the past century. We will also discuss some very recent developments and applications, such as the theory of  free boundary problems, emphasizing the synergy with other areas of mathematics.
Hosts: Lauren Ellison & Martha Precup