Two-dimensional Riemann problem for pressureless gas dynamics equations with functional solutions

The Riemann problem for a two-dimensional hyperbolic system of pressureless gas dynamics equations is considered here. Riemann solutions are constructed for any piecewise-constant initial data having two discontinuity rays with the origin as vertex. Non-classical waves (labelled as Dirac-shock waves) appear in some solutions. The entropy conditions for the Dirac-shock waves are given. Uniqueness of Riemann solutions containing Dirac-shock waves fails.