Signed sticky particles and 1D scalar conservation laws

We present an approximation of the entropy solution of a 1D scalar conservation law based on signed sticky particles when the variation of the initial condition is bounded. This method is a generalization of the one studied by Brenier and Grenier [2] in case the initial condition is monotone. When they collide, particles with the same sign stick together with conservation of the momentum whereas particles with opposite sign are destroyed. We prove the convergence of the approximate solution to the entropy solution when the initial number of particles goes to + ∞.