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Delta Shock Waves as Limits of Vanishing Viscosity for 2-D Steady Pressureless Isentropic Flow

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Yunnan University, Kunming, 650091, P.R. China

    Hongjun Cheng & Hanchun Yang

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  1. Hongjun Cheng
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  2. Hanchun Yang
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Correspondence to Hongjun Cheng.

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Supported by NNSF of China under Grant 10961025 and NSF of Yunnan province under Grant 2007A020M.

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Cheng, H., Yang, H. Delta Shock Waves as Limits of Vanishing Viscosity for 2-D Steady Pressureless Isentropic Flow. Acta Appl Math 113, 323–348 (2011). https://doi.org/10.1007/s10440-010-9602-6

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  • DOI: https://doi.org/10.1007/s10440-010-9602-6

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