Existence of traveling waves for the nonlocal Burgers equation

TL;DR

This paper proves the existence of traveling wave solutions for a nonlocal Burgers equation, generalizing a model for radiating gas and addressing an open question in the field.

Contribution

It introduces a monotone iteration scheme to establish traveling wave solutions for a broad class of nonlocal Burgers equations, extending previous results.

Findings

Existence of traveling waves for the nonlocal Burgers equation with arbitrary kernel K.

Solution construction via monotone iteration scheme.

Addresses an open question posed by Denis Serre.

Abstract

We study the equation $u_t +uu_x +u-K*u=0$ in the case of an arbitrary $K \geq 0$, which is a generalization of a model for radiating gas, in which $K(y)={1/2}e^{-|y|}$. 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.