Abstract |
【摘要】
The study of quasilinear hyperbolic partial differential equations (also known as conservation laws) presents formidable technical challenges. For example, the solutions to most initial-value problems have rather low regularity, and are found in function spaces which are themselves not easy to analyze. In a single space dimension, there is now a satisfactory theory, although it is limited to small data. In more than one space dimension, there is almost no theory.
In this presentation, I will give an overview of how technical difficulties in one space dimension have been overcome, emphasizing the underlying concepts that distinguish nonlinear from linear problems. This sets the stage for a description of the small amount of analysis that has been completed for conservation laws in two space dimensions, where the study of self-similar problems has yielded some rigorous results. I will illustrate with an exposition of a model problem involving Mach stems for a nonlinear wave equation. This example is joint work with Suncica Canic and Eun Heui Kin.
【簡介】
Barbara Lee Keyfitz is the Dr. Charles Saltzer Professor of Mathematics at the Ohio State University, which she joined in January 2009, after 21 years at the University of Houston and four and a half years as Director of the Fields Institute.
Barbara Keyfitz received her undergraduate education at 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 has contributed to the study of nonstrictly hyperbolic conservation laws. With Herbert Kranzer, she developed the concept of singular shocks, which occur in some types of systems.With Suncica Canic and others, she was a pioneer in the mathematical theory of self-similar solutions of multidimensional conservation laws.
She was President of the Association for Women in Mathematics in 2005-2006, a Vice-President of Society for Industrial and Applied Mathematics in 1998-2003. Now she is a Vice-President of the American Mathematical Society, and is in the middle of a four-year term as President of the International Council on Industrial and Applied Mathematics.
【榮譽與獎項】(僅列部份)
• SIAM Prize for Distinguished Service to the Profession, 2012.
• Fellow of the American Mathematical Society, 2012.
• Kovalevsky Lecturer at the AWM-SIAM Meeting, 2012.
• Noether Lecturer of the Association for Women in Mathematics, 2012.
• Fellow of the SIAM, 2010.
• Esther Farfel Award, University of Houston, 2006.
• Honorary Doctor Degree, the University of Waterloo, 2005.
• Krieger-Nelson Prize Lecture, Canadian Mathematical Society, 2005.
• Moores Professor, University of Houston, 1998-2008.
• Fellow of the American Association for the Advancement of Science, 1992. |