The linearization of a boundary value problem for a scalar conservation law. (English) Zbl 1158.35385

Caetano, Filipa

Commun. Math. Sci. 6, No. 3, 651-667 (2008).

Summary: 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.

MSC:

35L65	Hyperbolic conservation laws
35L50	Initial-boundary value problems for first-order hyperbolic systems
35R05	PDEs with low regular coefficients and/or low regular data
35L67	Shocks and singularities for hyperbolic equations

Keywords:

measure solutions; discontinuous coefficients; numerical schemes