Communications in Mathematical Sciences

The linearization of a boundary value problem for a scalar conservation law

Filipa Caetano

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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.

Article information

Commun. Math. Sci., Volume 6, Number 3 (2008), 651-667.

First available in Project Euclid: 29 September 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L65: Conservation laws 35L50: Initial-boundary value problems for first-order hyperbolic systems 35R05: Partial differential equations with discontinuous coefficients or data 76E99: None of the above, but in this section

Scalar conservation laws linearization boundary value problem shocks measure solutions


Caetano, Filipa. The linearization of a boundary value problem for a scalar conservation law. Commun. Math. Sci. 6 (2008), no. 3, 651--667.

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