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On some large systems of random particles which approximate scalar conservation laws. (English) Zbl 0846.35081

Summary: We build an \(N\)-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 \(L^1\) distance between the one-particle density function and its kinetic limit, using an appropriate joint process.

MSC:

35L65 Hyperbolic conservation laws
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