Axisymmetric solutions of a two-dimensional nonlinear wave system with a two-constant equation of state

Abstract

We study a special class of Riemann problem with axisymmetry for two-dimensional nonlinear wave equations with the equation of state $p=A_1\rho^{\gamma_1}+A_2\rho^{\gamma_2}$, $A_i<0$, $-3<\gamma_i<-1$ (i=1,2). The main difficulty lies in that the equations can not be directly reduced to an autonomous system of ordinary differential equations. To solve it, we use the axisymmetry and self-similarity assumptions to reduce the equations to a decoupled system which includes three components of solution. By solving the decoupled system, we obtain the structures of the corresponding solutions and their existence.

Keywords

• Nonlinear wave system
• generalized Chaplygin gas
• axisymmetry
• decoupled system