The Riemann problem to the stochastically perturbed non-viscous Burgers equation and the pressureless gas dynamics model

Abstract

Proceeding from the method of stochastic perturbation of a Langevin system associated with the non-viscous Burgers equation we construct a solution to the Riemann problem for the non-interacting particles and sticky particles systems. We analyze the difference in the behavior of discontinuous solutions for these two models and relations between them.