We state a kinetic formulation of weak entropy solutions of a general multidimensional scalar conservation law with initial and boundary conditions. We first associate with any weak entropy solution a entropy defect measure; the analysis of this measure at the boundary of the domain relies on the study of weak entropy sub and supersolutions and implies the introduction of the notion of sided boundary defect measures. As a first application, we prove that any weak entropy subsolution of the initial-boundary value problem is bounded above by any weak entropy supersolution (Comparison Theorem). We next study a BGK-like kinetic model that approximates the scalar conservation law. We prove that such a model converges by adapting the proof of the Comparison Theorem.
Publié le : 2004-07-05
Classification:
Conservation law,
initial-boundary value problem,
boundary defect measures,
kinetic traces,
weak entropy sub and supersolutions,
Comparison Theorem,
generalized kinetic solutions,
BGK-like kinetic model,
AMSC: 35L65, 35B50, 35D99, 35F25, 35F30, 35A35,
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-00176541,
author = {Imbert, Cyril and Vovelle, Julien},
title = {A kinetic formulation for multidimensional scalar conservation laws with boundary conditions and applications},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00176541}
}
Imbert, Cyril; Vovelle, Julien. A kinetic formulation for multidimensional scalar conservation laws with boundary conditions and applications. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00176541/