The linearized stability of solutions of nonlinear hyperbolic systems of conservation laws

We study the linearized stability of a discontinuous solution of a multidimensional hyperbolic system of conservation laws by linearizing the system around the basic solution; the resulting linearized system has discontinuous coefficients and involves nonconservative products. We propose a direct approach of the problem which introduces measure solutions and gives a natural meaning to the nonconservative product. This approach leads to simple numerical schemes.