Choques não-locais na variedade de ondas em sistemas quadráticos de duas leis de conservação

Abstract

Local Riemann solutions for quadratic systems of two conservation laws, in the geometric context of the wave manifold, were constructed. It is well known that characteristic $C$, sonic $S'$ and sonic $S$ are the boundaries of admissible shocks. In the first part of this work, we do a complete study on how Hugoniot curves intersect the sonic $S$ surface. In second part, we decompose the wave manifold into regions of admissibility of only local shocks and regions of admissibility of both local and non-local shocks. Important for this study was the introduction of a system of coordinates in which Hugoniot curves are straight lines, which is greatly simplify the characterization of the boundaries of admissible regions.