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

TL;DR

This paper develops a stochastic perturbation approach to solve the Riemann problem for non-viscous Burgers and pressureless gas dynamics, comparing solutions for non-interacting and sticky particles.

Contribution

It introduces a stochastic method to construct solutions for the Riemann problem in pressureless gas dynamics and analyzes differences between particle interaction models.

Findings

Constructed solutions for non-interacting particles

Analyzed differences between sticky and non-sticky particle solutions

Linked stochastic perturbation method to classical Riemann problem solutions

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.