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February 2002 Probabilistic Characteristics Method for a One-Dimensional Inviscid Scalar Conservation Law
B. Jourdain
Ann. Appl. Probab. 12(1): 334-360 (February 2002). DOI: 10.1214/aoap/1015961167


I this paper, we are interested in approxximation th entropy solution of a one-dimensional inviscid scalar conservation law starting from an initial condition with bounded variation owing to a system of interacting diffusions. We modify the system of signed particles associated with the parabolic equation obtained from the addition of a viscous term to this equation by killing couples of particles with opposite sign that merge. The sample paths of the corresponding reordered particles can be seen as probabilistic characteristic along which the approximate solution is constant. This enables us to prove that when the viscosity vanishes as the initial number of particles goes to $+\infty$, the approximate solution converges to the unique entropy solution of the inviscid conservation law. We illustrate this convergence by numerical results.


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B. Jourdain. "Probabilistic Characteristics Method for a One-Dimensional Inviscid Scalar Conservation Law." Ann. Appl. Probab. 12 (1) 334 - 360, February 2002.


Published: February 2002
First available in Project Euclid: 12 March 2002

zbMATH: 1013.60022
MathSciNet: MR1890068
Digital Object Identifier: 10.1214/aoap/1015961167

Primary: 65C35
Secondary: 60F17

Keywords: method of characteristics , propagation of chaos , reflected diffusion processes , Scalar conservation law , Stochastic particle systems

Rights: Copyright © 2002 Institute of Mathematical Statistics


Vol.12 • No. 1 • February 2002
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