Loading…

Delta Shock Waves as Flux-Approximation Limit of Solutions to the Modified Chaplygin Gas Equations

By introducing a triple parameter flux perturbation including pressure in the modified Chaplygin gas equations, we prove that, as the triple parameter flux perturbation vanishes, any two-shock Riemann solution and any two-rarefaction-wave Riemann solution to the perturbed modified Chaplygin gas equa...

Full description

Saved in:
Bibliographic Details
Published in:Acta applicandae mathematicae 2020-08, Vol.168 (1), p.75-107
Main Authors: Liu, Jinjing, Liang, Jie, Yang, Hanchun
Format: Article
Language:English
Subjects:
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:By introducing a triple parameter flux perturbation including pressure in the modified Chaplygin gas equations, we prove that, as the triple parameter flux perturbation vanishes, any two-shock Riemann solution and any two-rarefaction-wave Riemann solution to the perturbed modified Chaplygin gas equations tend to a delta-shock and a vacuum solution to the transport equations, respectively. Then we show that, as a double parameter flux perturbation vanishes, any two-shock Riemann solution under a certain condition to the perturbed modified Chaplygin gas equations tends to a delta shock wave solution to the generalized Chaplygin gas equations. In addition, we also show that, as a single parameter flux perturbation vanishes, any two-shock solution satisfying certain initial data and any parameterized delta shock wave solution to the perturbed generalized Chaplygin gas equations tend to a delta shock wave solution to the generalized Chaplygin gas equations. Finally, we exhibit some representative numerical simulations to confirm the theoretical analysis.
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-019-00280-2