Existence of a global smooth solution for a degenerate problem of the hyperbolic conservation law systems

Abstract

In this paper, we consider the existence of a global smooth solution for a degenerate problem of the hyperbolic conservation law systems. We use the characteristic decomposition to establish the global existence of smooth solutions to the degenerate Goursat problem up to a boundary and prove that the vacuum bubble is a point. This problem comes from the expansion of a wedge of gas with constant velocity into vacuum in gas dynamics.