Probabilistic model associated with the pressureless gas dynamics

2009/08/14 by Sergio Albeverio, Albeverio, Sergio, Anastasia Korshunova +3
Mathematics · #35L65 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #math.AP #math.PR #msc:35L65

paper · pdf · doi:10.48550/arxiv.0908.2084

28 pages, submitted

arxiv created 2009/09/07 · arxiv updated 2009/12/01

Abstract

Using a 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 pressureless gas dynamics describing sticky particles. As a bridging step we consider a medium consisting of noninteracting particles. We analyze the difference in the behavior of discontinuous solutions for these two models and the relations between them. In our framework we obtain a unique entropy solution to the Riemann problem in 1D case. Moreover, we describe how starting from smooth data a δ - singularity arises in one component of the solution.

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