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# Piecewise smooth solutions to the Burgers–Hilbert equation

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.

Paper:
Available as PDF (347 Kbytes).
Author(s):
Alberto Bressan
Tianyou Zhang
Submitted by:
; 2016-01-01.