EVOLUTION OF DISCONTINUITY AND FORMATION OF TRIPLE-SHOCK PATTERN IN SOLUTIONS TO A TWO-DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS

The evolution of discontinuity and formation of triple-shock pattern in solutions to a two-dimensional hyperbolic system of conservation laws are studied. When the initial discontinuity is a convex curve, it is discovered that the structure of the global solution changes dramatically around a critical time: After the critical time, a triple-shock pattern forms, while, before the critical time, only two shocks are developed. The envelope surface of intersections and the evolution of discontinuity are analyzed by developing new ideas and approaches. The global structure of the entropy solution is presented.