On some large systems of random particles which approximate scalar conservation laws

Article type: Research Article

Authors: Perthame, B.^; | Pulvirenti, M.

Affiliations: Université Paris VI, Laboratoire d'Analyse Numérique, 4 place Jussieu, F75252 Paris Cedex 05, France | Universitá di Roma I, Dipartimento di Matematica, Piazzale Aldo Moro, 2, 100100 Roma, Italy

Note: [] Correspondence to: B. Perthame, Université Paris VI, Laboratoire d'Analyse Numérique, 4 place Jussieu, F75252 Paris Cedex 05, France.

Abstract: We build aN-particle stochastic system subject to a multibody interaction. The postcollisional repartition is performed so that the one-particle density function solves a scalar conservation law in a suitable limit of hydrodynamical type. In the kinetic limit, we recover a relaxation model which approximates the scalar. conservation. law. Our proof relies on a direct estimate of the L1 distance between the one-particle density function and its kinetic limit, using an appropriate joint process.

DOI: 10.3233/ASY-1995-10304

Journal: Asymptotic Analysis, vol. 10, no. 3, pp. 263-278, 1995