The aim of this paper is to study a boundary value problem for a linear
scalar equation with discontinuous coefficients. This kind of problem
appears in the framework of the analysis of the linearized stability of a
fluid flow with respect to small perturbations of the boundary data. The
linear equation that we are interested in is obtained by linearizing the
equations which govern the flow, and involves discontinuous coefficients and
nontrivial products. We present a direct approach based on the one
introduced by Godlewski and Raviart, which leads to measure solutions, gives
a sense of these nontrivial products, and yields simple numerical schemes
that give good results.
Publié le : 2008-09-15
Classification:
Scalar conservation laws,
linearization,
boundary value problem,
shocks,
measure solutions,
35L65,
35L50,
35R05,
76E99
@article{1222716949,
author = {Caetano, Filipa},
title = {The linearization of a boundary value problem for a scalar conservation law},
journal = {Commun. Math. Sci.},
volume = {6},
number = {1},
year = {2008},
pages = { 651-667},
language = {en},
url = {http://dml.mathdoc.fr/item/1222716949}
}
Caetano, Filipa. The linearization of a boundary value problem for a scalar conservation law. Commun. Math. Sci., Tome 6 (2008) no. 1, pp. 651-667. http://gdmltest.u-ga.fr/item/1222716949/