Preprint 2016-001
Piecewise smooth solutions to the Burgers–Hilbert equation
Alberto Bressan and Tianyou Zhang
Abstract: The paper is concerned with the Burgers–Hilbert equation $u_t + (u^2/2)_x = \mathbf{H}[u]$, where the right hand side is a Hilbert transform. Unique entropy admissible solutions are constructed, locally in time, having a single shock. In a neighborhood of the shock curve, a detailed description of the solution is provided.