关键词: degenerate wave equations, Riemann problems, not strictly hyperbolic, Liu-entropy condition

Abstract:

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.

Key words: degenerate wave equations, Riemann problems, not strictly hyperbolic, Liu-entropy condition