September 23, 2022 - 2:30 PM to 3:30 PM
Dr. Khai T. Nguyen from North Carolina State University will give a colloquium talk on Sep 23 (Friday) from 2:30 pm to 3:30 pm in person at Fretwell 315. The title and abstract of the talk are given below.
Title: Shocks interaction for the Burgers-Hilbert Equation
Abstract: In 2009 J. Biello and J. Hunter derived a balance law modeling nonlinear waves with constant frequency, obtained from Burgers' equation by adding the Hilbert transform as a source term. For general L^2(R) initial data, the global existence of entropy weak solutions was proved by Bressan and Nguyen in 2014, together with a partial uniqueness result. Recently, unique piecewise continuous solutions with a single shock and the shock formation have been recently studied. This talk will describe a further type of local generic singularities for solutions, namely, points where two shocks interact.
Hope to see you at the talk.