Shock Profiles for the Shallow-Water Exner Models

This article is devoted to analyzing some ambiguities coming from a class ofsediment transport models. The models under consideration are governed by the couplingbetween the shallow-water and the Exner equations. Since the PDE system turnsout to be an hyperbolic system in non conservative form, ambiguities may occur assoon as the solution contains shock waves. To enforce a unique definition of the discontinuoussolutions, we adopt the path-theory introduced by Dal Maso, LeFLoch andMurat [18]. According to the path choices, we exhibit several shock definitions and weprove that a shock with a constant propagation speed and a given left state may connectan arbitrary right state. As a consequence, additional assumptions (coming fromphysical considerations or other arguments) must be chosen to enforce a unique definition.Moreover, we show that numerical ambiguities may still exist even when apath is chosen to select the system's solution.