Speaker: Prof. Alberto Bressan Eberly
Venue: Lecture Hall, 4th Floor, Run Run Shaw Business Administration Building
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 sourceterm. Recent work has established the global existence of solutions in the space L^2(R), and a partial result on uniqueness. This talk will also describe the construction of piecewise smooth solutions, locally in time, providing a detailed analysis of the solution profile in a neighborhood of each shock. Various related open problems will be discussed.