scholarly journals Asymptotic stability of rarefaction waves for a hyperbolic system of balance laws

2019 ◽  
Vol 12 (4) ◽  
pp. 923-944
Author(s):  
Kenta Nakamura ◽  
◽  
Tohru Nakamura ◽  
Shuichi Kawashima ◽  
◽  
...  
Keyword(s):  
Asymptotic Stability ◽  
Hyperbolic System ◽  
Balance Laws ◽  
Rarefaction Waves ◽  
System Of Balance Laws

scholarly journals Approximation of generalized Riemann solutions to compressible Euler-Poisson equations of isothermal flows in spherically symmetric space-times

2017 ◽  
Vol 48 (1) ◽  
pp. 73-94
Author(s):  
John Meng-Kai Hong ◽  
Reyna Marsya Quita
Keyword(s):  
Symmetric Space ◽  
Hyperbolic System ◽  
Local Source ◽  
Mixed System ◽  
Spherically Symmetric ◽  
Balance Laws ◽  
Conservation Of Mass ◽  
Poisson Equations ◽  
Compressible Euler ◽  
System Of Balance Laws

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 $3\times 3$ mixed-system of partial differential systems or a $2\times 2$ 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 $3\times 3$ 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.

ENTROPY-BASED MOMENT CLOSURE FOR KINETIC EQUATIONS: RIEMANN PROBLEM AND INVARIANT REGIONS

2006 ◽  
Vol 03 (04) ◽  
pp. 649-671 ◽  
Author(s):  
JEAN-FRANÇOIS COULOMBEL ◽  
THIERRY GOUDON
Keyword(s):  
Kinetic Equation ◽  
Riemann Problem ◽  
Hyperbolic System ◽  
Kinetic Equations ◽  
Moment Closure ◽  
Balance Laws ◽  
Nonlinear Hyperbolic System ◽  
Invariant Regions ◽  
System Of Balance Laws

We study a nonlinear hyperbolic system of balance laws that arises from an entropy-based moment closure of a kinetic equation. We show that the corresponding homogeneous Riemann problem can be solved without smallness assumption, and we exhibit invariant regions.

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