Delta shock wave with Dirac delta function in multiple components for the system of generalized Chaplygin gas dynamics

Boundary value problems

Yicheng Pang¹ 

[1]School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, China

关键词: delta shock wave;    generalized Chaplygin gas;    Euler equations;    Riemann problem;   

DOI  :  10.1186/s13661-016-0712-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We study the Riemann problem for the compressible Euler equations with the generalized Chaplygin gas. Based on the analysis on the physically relevant region, we obtain five kinds of exact solutions. It is shown that a delta shock wave with Dirac delta function in both density and internal energy develops in the exact solutions. The formation mechanism, generalized Rankine-Hugoniot relation and entropy condition are clarified for this type of delta shock wave. The numerical results are also presented to confirm this type of delta shock wave.

【 授权许可】

CC BY