Existence of traveling waves for the nonlocal Burgers equation

We study the equation ut+uux+u−K∗u=0ut+uux+u−K∗u=0 in the case of an arbitrary K≥0K≥0, which is a generalization of a model for radiating gas, in which K(y)=12e−|y|. Using a monotone iteration scheme argument we establish the existence of traveling waves, which gives a solution to an open question raised by D. Serre [L1L1-stability of nonlinear waves in scalar conservation laws, in: Evolutionary Equations, in: Handb. Differ. Equ., vol. I, North-Holland, Amsterdam, 2004, pp. 473–553].