Xianting Wang, Yun-Guang Lu, Qingyou Sun, Changfeng Xue, Solutions for a nonstrictly hyperbolic and genuinely nonlinear system

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DOI: 10.23952/jnva.7.2023.2.02

Volume 7, Issue 2, 1 April 2023, Pages 201-207

Abstract. In this paper, we study the existence of global entropy solutions for the Cauchy problem of an isentropic gas dynamics system with the special pressure $P(\rho)= \frac{1}{1-\rho}$ . After the gas density $\rho$ is fixed in the region $\rho \in (0,1)$ , by the method of the artificial viscosity and the maximum principle, this system is nonstrictly hyperbolic and genuinely nonlinear, and its global entropy solutions are obtained by the famous compactness framework introduced by DiPerna in the paper “Convergence of approximate solutions to conservation laws” (Arch. Rat. Mech. Anal., (82) (1983), 27-70).

How to Cite this Article:
X. Wang, Y.G. Lu, Q. Sun, C. Xue, Solutions for a nonstrictly hyperbolic and genuinely nonlinear system, J. Nonlinear Var. Anal. 7 (2023), 201-207.