The riemann problem for the nonlinear degenerate wave equations

In this paper we consider the Riemann problem for the nonlinear degenerate wave equations. This problem has been studied by Sun and Sheng, however the so-called degenerate shock solutions did not satisfy the R-H condition. In the present paper, the Riemann solutions of twelve regions in the v – u plane are completely constructed by the Liu-entropy condition. Our Riemann solutions are very different to that one obtained by Sun and Sheng in some regions.