Kinetics of shock clustering with piecewise-deterministic data
Series: Mathematical Physics and Probability Seminar
Location: Math 402
Presenter: David Kaspar, Arizona State University
Statistical descriptions of solutions to Burgers' equation with various Markov process initial data have been the subject of several investigations in the 1990s, culminating in a remarkable work of Bertoin showing that Levy processes are preserved, together with a characterization of the evolution of the associated jump measures. Menon and Srinivasan conjectured a similar result for more general scalar conservation laws. We discuss a kinetic statistical description of solutions for scalar conservation laws with certain piecewise-deterministic Markov initial data. This work is joint with Fraydoun Rezakhanlou (UC Berkeley).