Communications in Mathematical Sciences

Volume 20 (2022)

Number 6

Stability of non-degenerate stationary solution in inflow problem for a 1-D radiation hydrodynamics model

Pages: 1763 – 1783



Kwang-Il Choe (School of Economics and Management, University of Science and Technology Beijing, China; and School of Mathematics, University of Mechanical Engineering, Pyongyang, D.P.R. Korea)

Hakho Hong (Institute of Mathematics, State Academy of Sciences, Pyongyang, D.P.R. Korea)

Jongsung Kim (School of Mathematics, University of Mechanical Engineering, Pyongyang, D.P.R. Korea)


This paper is concerned with the large-time behavior of the solutions to the inflow problem for a 1‑D compressible viscous heat-conducting gas with radiation in the half line $(0,\infty)$. We first give the existence of non-degenerate (supersonic and subsonic) stationary solutions with the aid of center manifold theory. In addition, using an energy method, we show the time-asymptotic stability of the non-degenerate stationary solutions under smallness assumptions on the initial perturbation and the boundary data in the Sobolev space.


compressible radiation hydrodynamics, inflow problem, stationary solution, stability

2010 Mathematics Subject Classification

35B35, 35Q30, 76D33, 76N10, 78A40

Author contributions. All persons who meet authorship criteria are listed as authors, and all authors certify that they have participated sufficiently in the work to take public responsibility for the content, including participation in the concept, design, analysis, writing, or revision of the manuscript. Furthermore, each author certifies that this material or similar material has not been and will not be submitted to or published in any other publication.

Conflict of interest. No conflict of interest exists. The authors wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

Received 3 November 2021

Accepted 21 January 2022

Published 14 September 2022