Existence of traveling waves for the nonlocal Burgers equation

Abstract

We study the equation $u_t+u{u}_x+u-K\ast u=0$ in the case of an arbitrary $K\ge 0$, which is a generalization of a model for radiating gas, in which $K(y)=1/2e^{-|y|}$. Using a monotone iteration scheme argument we establish the existence of traveling waves, which gives a solution to an open question raised by Denis Serre.

arXiv comment5 pages, submitted to Applied Mathematics Letters