Systems of Sticky Particles Governed by Burgers' Equation

We show the existence of two sticky particles models with the same velocity function () which is the entropy solution of the inviscid Burgers' equation. One of them is governed by the set of discontinuity points of 0. Thus, the trajectories ↦ coincide; however one has different mass distributions =d0∘−1 and ∘−1. Here, denotes the Lebesgue measure.