Methods and Applications of Analysis
Volume 28 (2021)
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
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.
viscous radiative and reactive gas, contact discontinuity, nonlinear stability, large initial perturbation
2010 Mathematics Subject Classification
35L65, 35Q35, 76N15, 76V05
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