Burgers' equation and the sticky particles model

Under general assumptions on the initial data, we show that the entropy solution (x, t) bar right arrow u(x, t) of the one-dimensional inviscid Burgers' equation is the velocity function of a sticky particles model whose initial mass distribution is Lebesgue measure. Precisely, the particles trajectories (x, t) bar right arrow X-0,X- t(x) are given by a forward flow: for all (x, s, t) is an element of R x R+ x R+, X-0,X-s+t(x) = X-s,X-t(X-0,X-s(x)) and partial derivative/partial derivative t X-s,X-t = u(X-s,X-t, s + t) = E[u(., s)vertical bar X-s,X-t]; u(x, t) = E[u(., 0)vertical bar X-0,X-t = x]. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4729540]