Communications in Mathematical Sciences

Volume 15 (2017)

Number 5

Global solutions to one-dimensional equations for a self-gravitating viscous radiative and reactive gas with density-dependent viscosity

Pages: 1423 – 1456



Yongkai Liao (School of Mathematics and Statistics, Wuhan University, Wuhan, China)

Huijiang Zhao (School of Mathematics and Statistics, and Hubei Key Laboratory, Wuhan University, Wuhan, China)


In this paper we are concerned with the global existence of smooth solutions to two types of initial-boundary value problems to a system of equations describing one-dimensional motion of self-gravitating, radiative and chemically reactive gas whose viscosity coefficient depends on density. The main ingredient of the analysis is to derive the positive lower and upper bounds on both the specific volume and the absolute temperature.


global solutions, self-gravitating viscous radiative and reactive gas, density-dependent viscosity, density- and temperature-dependent heat conductivity

2010 Mathematics Subject Classification

35D35, 35Q35, 76D05, 76V05

This work was supported by a grant from National Natural Science Foundation of China under contract 11671309 and the Fundamental Research Funds for the Central Universities.

Received 12 October 2016

Published 26 June 2017