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September 2008 The linearization of a boundary value problem for a scalar conservation law
Filipa Caetano
Commun. Math. Sci. 6(3): 651-667 (September 2008).


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.


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Filipa Caetano. "The linearization of a boundary value problem for a scalar conservation law." Commun. Math. Sci. 6 (3) 651 - 667, September 2008.


Published: September 2008
First available in Project Euclid: 29 September 2008

zbMATH: 1158.35385
MathSciNet: MR2455469

Primary: 35L50 , 35L65 , 35R05 , 76E99

Keywords: boundary value problem , Linearization , measure solutions , Scalar conservation laws , shocks

Rights: Copyright © 2008 International Press of Boston

Vol.6 • No. 3 • September 2008
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