Monday, April 1, 11:00AM-12:00 Noon, Fretwell 315

March 15, 2019 by Duan Chen
Categories: Spring 2022
Professor Khai Nguyen  Dept.  of Mathematics, NC State University
Title: Kolmogorov Entropy Compactness Estimates for nonlinear PDEs
Abstract. Inspired by a question posed by Lax in 2002, in recent years it
has received an increasing attention the study on the quantitative analysis of
compactness for nonlinear PDEs. In this talk, I will present recent results on
the sharp compactness estimates in terms of Kolmogorov epsilon entropy for
hyperbolic conservation laws and Hamilton-Jacobi equations. Estimates of this
type play a central roles in various areas of information theory and statistics as
well as of ergodic and learning theory. In the present setting, this concept could
provide a measure of the order of “resolution” of a numerical method for the
corresponding equations.