Shadow waves: entropies and interactions for delta and singular shocks

Abstract

The paper deal with two key problems for delta (or singular) shock so- lutions to systems of conservation laws: entropy admissibility conditions for them (which is connected to the notorious uniqueness problem) and their interaction. A way we chose is to represent them by nets of piecewise constant (or constant with respect only to the space variable) functions, here called shadow waves. All the calculations then can be done on each element of such net using the usual Rankine-Hugoniot conditions only. The 3 × 3 pressureless gas dynamics model is the main example in the paper.