Premium
The Riemann problem for the Chaplygin gas equations with a source term
Author(s) -
Shen Chun
Publication year - 2016
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201500015
Subject(s) - chaplygin gas , term (time) , riemann hypothesis , shock wave , physics , momentum (technical analysis) , degree rankine , classical mechanics , mathematical physics , riemann problem , shock (circulatory) , coulomb , dirac delta function , mechanics , mathematical analysis , mathematics , quantum mechanics , cosmology , medicine , finance , economics , electron , dark energy
The Riemann solutions for the one‐dimensional Chaplygin gas equations with a Coulomb‐like friction term are constructed explicitly. It is shown that the delta shock wave appears in the Riemann solutions in some certain situations. The generalized Rankine‐Hugoniot conditions of delta shock wave are established and the position, propagation speed and strength of delta shock wave are given, which enables us to see the influence of Coulomb‐like friction term on the Riemann solutions for the Chaplygin gas equations clearly. In addition, the relations connected with the area transportation are derived which include mass and momentum transportation.