Professor Khai Nguyen Dept. Mathematics, NC State University
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 leaning theory. In the present setting, this concept could provide a measure of the order of "resolution" of a numerical method for the corresponding equations.