Systems of sticky particles governed by Burgers' equation (Q764760)

Summary: We show the existence of two sticky particles models with the same velocity function \(u_t(x)\) which is the entropy solution of the inviscid Burgers' equation. One of them is governed by the set of discontinuity points of \(u_0\). Thus, the trajectories \(t \rightarrowtail X_t\) coincide; however one has different mass distributions \(\sigma_x u_t = du_0 \circ X^{-1}_t\) and \(\lambda \circ X^{-1}_t\) Here, \(\lambda\) denotes the Lebesgue measure.