Methods and Applications of Analysis

Volume 28 (2021)

Number 3

Special issue dedicated to Professor Ling Hsiao on the occasion of her 80th birthday, Part II

Guest editors: Qiangchang Ju (Institute of Applied Physics and Computational Mathematics, Beijing), Hailiang Li (Capital Normal University, Beijing), Tao Luo (City University of Hong Kong), and Zhouping Xin (Chinese University of Hong Kong)

Contact discontinuity for a viscous radiative and reactive gas with large initial perturbation

Pages: 265 – 298

DOI: https://dx.doi.org/10.4310/MAA.2021.v28.n3.a2

Authors

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

Zhendong Xu (Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, China)

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

Abstract

This paper is concerned with the time-asymptotically nonlinear stability of contact discontinuity to the Cauchy problem of a one-dimensional viscous radiative and reactive gas with large initial perturbation. Our main idea is to use the smallness of the strength of the contact discontinuity to control the possible growth of its solutions induced by the nonlinearity of the system and interactions between the solutions and the contact discontinuity. The key point in our analysis is to obtain the uniform positive lower and upper bounds on the specific volume and the absolute temperature.

Keywords

viscous radiative and reactive gas, contact discontinuity, nonlinear stability, large initial perturbation

2010 Mathematics Subject Classification

35L65, 35Q35, 76N15, 76V05

Full Text (PDF format)

This work was partially supported by a grant from the Natural Science Foundation of Hubei Province under contract 2019CFA007, and by two grants from the National Natural Science Foundation of China under contracts 11731008 and 11671309, respectively.

Received 24 December 2019

Accepted 4 June 2020

Published 10 June 2022