Communications in Mathematical Sciences

Volume 18 (2020)

Number 8

Stability of a composite wave of viscous contact wave and rarefaction waves for radiative and reactive gas without viscosity

Pages: 2191 – 2213



Guiqiong Gong (School of Mathematics and Statistics, Wuhan University, Wuhan, China)

Lin He (College of Mathematics, Sichuan University, Chengdu, China)


The Cauchy problem of the 1D compressible radiative and reactive gas without viscosity is studied in this paper. When the radiation effect is under consideration, the equations present high nonlinearity, together with the lack of viscosity, which result in many more difficulties. When the solution to the corresponding Riemann problem of the Euler equation consists of a contact discontinuity and rarefaction waves, we proved that there exists a unique global-in-time solution and which tends to the combination of a viscous contact wave and rarefaction waves asymptotically with small initial data. The proof is given by the elementary energy method.


contact wave, rarefaction wave, radiative and reactive gas, non-viscous, nonlinear stability

2010 Mathematics Subject Classification

35B40, 35Q35

Guiqiong Gong was supported by the grants from the National Natural Science Foundation of China under contracts 11731008 and 11671309. Lin He is partially supported by the Fundamental Research Funds for the Central Universities No. YJ201962.

Received 18 December 2019

Accepted 8 June 2020

Published 22 December 2020