HYPERBOLIC EQUATIONS AND SYSTEMS WITH DISCONTINUOUS COEFFICIENTS OR SOURCE TERMS

Abstract. This paper is devoted to the study of some nonlinear hyperbolic equations or systems with discontinuous coefficients or with source terms. The common feature of the considered problems is the fact that the jacobian matrix of an associated autonomous system is not diagonalizable in R for many values of the unknown (leading to linear ill posed problems). However, the nonlinear problems appear to be well posed (at least numerically, in the case of systems) in usual functional spaces, even for discontinuous solutions