Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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DELTA-SHOCK FOR THE NONHOMOGENEOUS PRESSURELESS EULER SYSTEM

  • Shiwei Li (College of Science Henan University of Engineering) ;
  • Jianli Zhao (College of Science Henan University of Engineering)
  • Received : 2023.05.21
  • Accepted : 2023.09.05
  • Published : 2024.05.31
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Abstract

We study the Riemann problem for the pressureless Euler system with the source term depending on the time. By means of the variable substitution, two kinds of Riemann solutions including deltashock and vacuum are constructed. The generalized Rankine-Hugoniot relation and entropy condition of the delta-shock are clarified. Because of the source term, the Riemann solutions are non-self-similar. Moreover, we propose a time-dependent viscous system to show all of the existence, uniqueness and stability of solutions involving the delta-shock by the vanishing viscosity method.

Keywords

Acknowledgement

This paper is supported by the Ph.D. Foundation of Henan University of Engineering (D2022028), the Science and Technology Research Program of Education Department of Henan Province (22A110008). The author Shiwei Li would like to thank Professor Hanchun Yang, his advisor, for some valuable and inspiring discussions and suggestions.

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