TY - JOUR

T1 - Approximation of generalized riemann solutions to compressible euler-poisson equations of isothermal flows in spherically symmetric space-times

AU - Hong, John M.

AU - Quita, Reyna Marsya

PY - 2017/3

Y1 - 2017/3

N2 - 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.

AB - 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.

KW - Approximate generalized solutions

KW - Compressible Euler-Poisson equations

KW - Generalized Riemann problem

KW - Initial-boundary value problem

KW - Lax method

KW - Linearized hyperbolic systems

UR - http://www.scopus.com/inward/record.url?scp=85014423980&partnerID=8YFLogxK

U2 - 10.5556/j.tkjm.48.2017.2274

DO - 10.5556/j.tkjm.48.2017.2274

M3 - 期刊論文

AN - SCOPUS:85014423980

SN - 0049-2930

VL - 48

SP - 73

EP - 94

JO - Tamkang Journal of Mathematics

JF - Tamkang Journal of Mathematics

IS - 1

ER -