Shadow waves: Entropies and interactions for delta and singular shocks

Abstract

This paper deals with two key problems for delta (or singular) shock solutions to systems of conservation laws: that of their entropy admissibility conditions (which is connected to the notorious uniqueness problem) and that of their interaction. We choose to represent systems of conservation laws by nets of functions which are piecewise constant (or constant with respect only to the space variable), here called shadow waves. All the calculations can then be done on each element of such nets using only the usual Rankine-Hugoniot conditions. A 3 × 3 pressureless gas dynamics model is the main example in the paper. © 2009 Springer-Verlag.