## The Calvin and Jean Long Distinguished Lecture in Mathematics

# Dr. Barbara Lee Keyfitz

### "Partial Differential Equations: What Do We Know When We Know that a Solution Exists?"

#### Thursday, October 12, 2017

7:00pm in Webster 17

Please join us for an informative discussion by this year's invited guest lecturer **Dr. Barbara Lee Keyfitz**, a Dr. Charles Saltzer Professor of Mathematics from Ohio State University.

**Abstract:**

In elementary mathematics, solving a problem often means finding a formula for the solution. However, for problems that lead to differential equations very often there is not a formula. Mathematicians may work hard to convince themselves, and their community, that a solution does nonetheless exist, but the wider world is often unconvinced that they have learned anything from this information. In this talk, I will demonstrate with examples (not proofs!) how demonstrating that solutions to a problem exist can give insight into the nature of the problem, and the nature of the solution, even if the details of a particular solution can be found only approximately, for example by numerical simulation. The conclusion is that the payoff for analysing a partial differential equation goes well beyond an exercise in analysis.

**Reception:**

Immediately following the lecture we invite you to join us for refreshments in Neill Hall 216 (Hacker Lounge).

**About Dr. Keyfitz:**

Dr. Keyfitz joined the Department of Mathematics at Ohio State University after 25 years at the University of Houston. From July 2004 until December 2008 she was Director of the Fields Institute for Research in Mathematical Sciences in Toronto, Canada. Her research is in the field of nonlinear partial differential equations. She has studied systems of conservation laws which are nonstrictly hyperbolic or which change type from hyperbolic to elliptic in steady or unsteady flow. Systems with this behavior arise in models for multiphase flow in porous media, and in two-phase compressible and incompressible flow. With Suncica Canic and Eun Heui Kim, she began an analysis of self-similar solutions of systems of conservation laws in two space dimensions. Recently, she has been working with Katarina Jegdic and with Allen Tesdall on extensions of this multidimensional work.

From October 1, 2009 to September 30, 2015 she served as President-Elect of the International Council on Industrial and Applied Mathematics (ICIAM).