Systems of Sticky Particles Governed by Burgers' Equation

Abstract EN

We show the existence of two sticky particles models with the same velocity function ut(x) which is the entropy solution of the inviscid Burgers' equation.

One of them is governed by the set of discontinuity points of u0.

Thus, the trajectories t↦Xt coincide; however one has different mass distributions ∂xut=du0∘Xt-1 and λ∘Xt-1.

Here, λ denotes the Lebesgue measure.