A nonlocal version of wavefront tracking motivated by Kuramoto-Sakaguchi equation

In this paper, we present a modified wave-front tracking algorithm which is suitable for the analysis of scalar conservation laws with nonlocal terms. This method has been first employed in [14] to analyze a nonlocal Hamilton-Jacobi equa- tion related to a granular flow and later used in other works. Such an approach leads to a possibly simpler analysis in obtaining rigorous quantitive estimates on approx- imate solutions, compared to a classical iteration procedure based on the recompu- tation of the nonlocal term at each time step. Here, we delineate this method for a nonlocal equation namely “the Kuramoto-Sakaguchi equation” arising from the ki- netic modeling of collective motion of large ensemble of Kuramoto oscillators, for which BV-weak solutions and their large time behavior are investigated in [2].