About uniqueness to first order
By Nieto, Poupaud and Soler.
In this work we give a criterion to discriminate the entropy solution to quasi-linear equations of first order among weak solutions. This uniqueness statement is a generalization of Oleinik's criterion, which makes reference to the measure of the increasing character of weak solutions.
The link between Oleinik's criterion and the entropy condition due to Kruzhkov is also clarified.
An application of this analysis to the convergence of the particle method for conservation laws is also given by using the Filippov characteristics.