The linearized stability of solutions of nonlinear hyperbolic systems of conservation laws - A general numerical approach

We study the linearized stability of a discontinuous solution of a multidim ensional hyperbolic system of conservation laws by linearizing the system a round the basic solution; the resulting linearized system has discontinuous coefficients and involves nonconservative products. We propose a direct ap proach of the problem which introduces measure solutions and gives a natura l meaning to the nonconservative product. This approach leads to simple num erical schemes. (C) 1999 IMACS/Elsevier Science B.V. All rights reserved.