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Generalized plane delta shock waves for the n-dimensional zero-pressure gas dynamics with energy conservation law

Author

Listed:
  • Yanyan Zhang

    (Xinyang Normal University)

  • Yu Zhang

    (Yunnan Normal University)

Abstract

By virtue of the generalized plane wave solution, we study a type of generalized plane delta shock wave for the n-dimensional zero-pressure gas dynamics governed by the conservation of mass, momentum and energy. It is found that a special kind of generalized plane delta shock wave on which both state variables simultaneously contain the Dirac delta functions appears in Riemann solutions, which is significantly different from the customary ones on which only one state variable contains the Dirac delta function. The generalized Rankine-Hugoniot relation of the generalized plane delta shock wave is derived. Under a suitable entropy condition, we further solve a kind of n-dimensional Riemann problem with Randon measure as initial data, and four different explicit configurations of solutions are constructively established. Finally, the overtaking of two plane delta shock waves is analyzed.

Suggested Citation

  • Yanyan Zhang & Yu Zhang, 2019. "Generalized plane delta shock waves for the n-dimensional zero-pressure gas dynamics with energy conservation law," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(4), pages 1067-1086, December.
    • Handle: RePEc:spr:indpam:v:50:y:2019:i:4:d:10.1007_s13226-019-0374-z
    DOI: 10.1007/s13226-019-0374-z
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