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.
Publié le : 2002-02-14
Classification:
Scalar conservation law,
method of characteristics,
stochastic particle systems,
reflected diffusion processes,
propagation of chaos,
65C35,
60F17
@article{1015961167,
author = {Jourdain, B.},
title = {Probabilistic Characteristics Method for a One-Dimensional
Inviscid Scalar Conservation Law},
journal = {Ann. Appl. Probab.},
volume = {12},
number = {1},
year = {2002},
pages = { 334-360},
language = {en},
url = {http://dml.mathdoc.fr/item/1015961167}
}
Jourdain, B. Probabilistic Characteristics Method for a One-Dimensional
Inviscid Scalar Conservation Law. Ann. Appl. Probab., Tome 12 (2002) no. 1, pp. 334-360. http://gdmltest.u-ga.fr/item/1015961167/