Linear and Nonlinear Stability of Shocks: Some of the Things I Learned From Karen Ames

Dr. Karen A. Ames Lecture Series on Applied Mathematics

Dr. Barbara Lee Keyfitz

Department of Mathematics
The Ohio State University


3:00 Friday, 3 April 2009

219 Shelby Center
Refreshments at 2:30

Abstract

Shocks (nonlinear discontinuities) separating a region of hyperbolic states from a non-hyperbolic region can occur in one of two ways in conservation laws. Steady transonic flow is a well-known phenomenon, and transonic shocks appear to be both physically and mathematically stable. Unsteady non-hyperbolic systems, on the other hand, would seem to form ill-posed, even catastrophically ill-posed problems. In this talk, I will review some work that Karen Ames and I did that suggested a sense in which shocks in these ill-posed systems may enjoy a type of stability. Later work with Milton Lopes has confirmed our initial, linear results.

colloq KeyfitzBiographical Sketch

Dr. Barbara Lee Keyfitz joined the Department of Mathematics at Ohio State in 2009, after 20 years at the University of Houston and 4 ½ years as Director of the Fields Institute in Toronto, Canada. She received her Bachelor's degree from the University of Toronto and her M.S. and Ph.D. from the Courant Institute, New York University. Her research area is Nonlinear Partial Differential Equations. She is a Fellow of the American Association for the Advancement of Science, and was the recipient of the 2005 Krieger-Nelson Prize of the Canadian Mathematical Society. In the past, Dr. Keyfitz has served as a faculty member at the University of Houston, Columbia University, Princeton University, and Arizona State University. She has held visiting positions at the University of Nice, Duke University, UC Berkley, Institute for Mathematics and Its Applications, the Fields Institute, and Brown University. In 2005-06, Dr. Keyfitz served as the President of the Association for Women in Mathematics and is the Treasurer of the International Council on Industrial and Applied Mathematics.