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

Date

2017-06-28

Authors

Wang, Guodong
Hu, Yanbo
Liu, Huayong

Journal Title

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Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

We study a special class of Riemann problem with axisymmetry for two-dimensional nonlinear wave equations with the equation of state p = A1ργ1 + A2ργ2, Ai < 0, -3 < yi < -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.

Description

Keywords

Nonlinear wave system, Generalized Chaplygin gas, Axisymmetry, Decoupled system

Citation

Wang, G., Hu, Y., & Liu, H. (2017). Axisymmetric solutions of a two-dimensional nonlinear wave system with a two-constant equation of state. <i>Electronic Journal of Differential Equations, 2017</i>(156), pp. 1-18.

Rights

Attribution 4.0 International

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