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The Riemann problem for the two-dimensional steady pressureless isentropic flow in gas dynamics is solved completely. The Riemann solutions contain two kinds: delta-shock solutions and vacuum solutions. Under suitable generalized Rankine-Hugoniot relation and entropy condition, the existence and uniqueness of delta-shock solutions is established. Moreover, the stability of delta-shock solution to a reasonable viscous perturbation is proven. The numerical results coinciding with the theoretical solutions are also presented.
Acta Applicandae Mathematicae – Springer Journals
Published: Jan 13, 2011
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