PDE Lecture Series, February 24-26, 2020
TITLE: Relative entropy method for conservation laws
SPEAKER: Alexis Vasseur, University of Texas at Austin
Lecture 1: Monday, 2/24, 3pm-4pm, Thackeray Hall 427
Lecture 2: Tuesday, 2/25, 11:30am-12:30pm, Thackeray Hall 427
Lecture 3: Tuesday, 2/25, 3pm-4pm, Thackeray Hall 427
Lecture 4: Wednesday, 2/26, 3pm-4pm, Thackeray Hall 427
ABSTRACT: We will present a general theory to study the stability of shocks for conservation laws. It deviates from the standard theory, since it is not based on the integrated equation, nor any kind of linearization. This allows to consider even situations with large perturbations. The theory provides a contraction up to a shift, based on the relative entropy. It can be applied also to 1D compressible Navier-Stokes equations, to obtained stability a viscous shocks uniformly with respect to the viscosity (even in the inviscid limit to the Euler equation). In this lecture, we will focus on the scalar case, where the results are easier to describe. However, we will sketch how the result can be extended to the system case.