Approximation of generalized riemann solutions to compressible euler-poisson equations of isothermal flows in spherically symmetric space-times

John M. Hong, Reyna Marsya Quita

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we consider the compressible Euler-Poisson system in spherically symmetric space-times. This system, which describes the conservation of mass and momentum of physical quantity with attracting gravitational potential, can be written as a 3×3 mixed-system of partial differential systems or a 2×2 hyperbolic system of balance laws with global source. We show that, by the equation for the conservation of mass, Euler-Poisson equations can be transformed into a standard 3×3 hyperbolic system of balance laws with local source. The generalized approximate solutions to the Riemann problem of Euler-Poisson equations, which is the building block of generalized Glimm scheme for solving initial-boundary value problems, are provided as the superposition of Lax's type weak solutions of the associated homogeneous conservation laws and the perturbation terms solved by the linearized hyperbolic system with coefficients depending on such Lax solutions.

Original languageEnglish
Pages (from-to)73-94
Number of pages22
JournalTamkang Journal of Mathematics
Volume48
Issue number1
DOIs
StatePublished - Mar 2017

Keywords

  • Approximate generalized solutions
  • Compressible Euler-Poisson equations
  • Generalized Riemann problem
  • Initial-boundary value problem
  • Lax method
  • Linearized hyperbolic systems

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