We consider the problem of constructing systems of hyperbolic conservation laws in one space dimension with prescribed eigencurves. This yields an overdetermined system of equations for the eigenvalues-to-be. These equations are analyzed with techniques from exterior differential systems.

We provide an informal overview on the theory of transport equations with non smooth velocity fields, and on some applications of this theory to the well-posedness of hyperbolic systems of conservation laws.

We are concerned with the asymptotic behavior of entropy solutions of nonlinear conservation laws. The main objective of this paper is to present an analytical approach and to explore its applications to studying the large-time behavior of periodic entropy solutions of hyperbolic conservation laws. The asymptotic decay of periodic solutions of nonlinear hyperbolic conservation laws is an import...