On the Global Existence of the Solutions of the Riemann Problem for Shallow Water Equations

Abstract

In this talk we investigate the Riemann Problem for a shallow water model with vegetation and terrain data. We present a constructive method, that is not dependent on how large data jump is, to solve the problem. Essentially the method involves the resolution of a nonlinear equation that can have multiple solutions or no solution. The method uses a criterion of admissibility to select among multiple possible solutions a physical relevant one. To illustrate the method several examples are presented.