The Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations with a source term. (June 2018)

• Record Type: Journal Article
• Authors: Guo, Lihui; Li, Tong; Pan, Lijun; Han, Xinli
• Is Part Of: Nonlinear analysis. Volume 41(2018)
• Page Start: 588
• Page End: 606
• Publication Date: 2018-06
• Subjects: Riemann problem -- Delta initial data -- Chaplygin gas equations -- Coulomb-like friction term -- Non self-similar -- Delta shock wave; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.11.013
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations with a friction term is considered. Unlike the homogeneous case, the Riemann solutions are no longer self-similar due to the influence of the source term. In particular, delta contact discontinuities are found in the Riemann solutions with delta initial data for the Chaplygin gas equations with the source term. Moreover, we discover that the Chaplygin gas equations can be transformed to the equations of string motion in Minkowski space. The delta shock wave can explain the appearance of the singularities developed in the motion of the string.