Hyperbolic Systems of Converstaion Laws

Abstract

Conservation laws are first order systems of quasilinear partial differential equations in divergence form; they express the balance laws of continuum physics for media with “elastic” response, in which internal dissipation is neglected. The absence of internal dissipation is manifested in the emergence of solutions with jump discontinuities across manifolds of codimension one, representing, in the applications, phase boundaries or propagating shock waves. The presence of discontinuities makes the analysis hard; the redeeming feature is that solutions are endowed with rich geometric structure. Indeed, the most interesting results in the area have a combined analytic-geometric flavor.