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Shadow waves: Entropies and interactions for delta and singular shocks. (English) Zbl 1201.35134

The author considers the conservation law

${\partial }_{t}f\left(U\right)+{\partial }_{x}g\left(U\right)=0$

with $U:{ℝ}_{+}^{2}\to {ℝ}^{n}$, $f,g:{ℝ}^{n}\to {ℝ}^{n}$. The focus is on the delta and singular shock solutions of the Riemann problem, their entropy admissibility conditions, and their interaction. The system is represented by piecewise constant functions called shadow waves. An example of three-dimensional pressureless gas dynamics is considered.

##### MSC:
 35L67 Shocks and singularities 35L65 Conservation laws 76L05 Shock waves; blast waves (fluid mechanics)
##### References:
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