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Evolution of discontinuity and formation of triple-shock pattern in solutions to a two-dimensional hyperbolic system of conservation laws. (English) Zbl 1183.35227

Summary: 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.

MSC:

35Q35 PDEs in connection with fluid mechanics
76G25 General aerodynamics and subsonic flows
35L65 Hyperbolic conservation laws
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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