Open AccessOn the delta shockwave interactions for the isentropic Chaplygin gas system consisting of three scalar equations
Author(s) -
Meina Sun,
Jie Xin
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1916355s
Subject(s) - riemann problem , riemann hypothesis , chaplygin gas , mathematics , isentropic process , shock wave , mathematical analysis , classification of discontinuities , riemann's differential equation , piecewise , euler system , euler equations , scalar (mathematics) , mathematical physics , riemann xi function , physics , mechanics , geometry , quantum mechanics , cosmology , dark energy
The Riemann problem for the one-dimensional version of isentropic compressible Euler system for the Chaplygin gas consisting of three scalar equations is considered. It is shown that the Riemann solutions involve only two situations: the combination of three contact discontinuities or a delta shock wave. The generalized Rankine-Hugoniot conditions of delta shock wave are derived and the exact delta shock wave solution including the strength and propagation speed is obtained explicitly. The solutions to the perturbed Riemann problem are constructed globally when the initial data are taken to be the three piecewise constant initial data. The wave interaction problem is extensively investigated and some interesting phenomena are observed. It is shown that the limits of solutions to the perturbed Riemann problem converge to the corresponding ones to the Riemann problem when the perturbation parameter tends to zero.