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Umehara, M. and Tani, A. (2008) Global Solvability of the Free-Boundary Problem for One-Dimensional Motion of a Self-Gravitating Viscous Radiative and Reactive Gas. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 84, 123-128.
https://doi.org/10.3792/pjaa.84.123

has been cited by the following article:

• TITLE: Time-Periodic Solutions of the Hydrodynamic Equations for a Reacting Mixture in n-Dimension

  AUTHORS: Chenhan Wang

  KEYWORDS: Time-Periodic Solutions, Compressible Navier-Stokes Equation, Radiative and Reactive Gases, Decay Rate

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.12 No.4, April 29, 2022

  ABSTRACT: In this paper, we investigate the existence of time-periodic solutions to the n-dimension hydrodynamic model for a reacting mixture with a time-periodic external force when the dimension is under some smallness assumption. The energy method combined with the spectral analysis is used to obtain the optimal decay estimates on the linearized solution operator. We study the existence and uniqueness of the time-periodic solution in some suitable function space by using a fixed point method and the decay estimates. Furthermore, we obtain the time asymptotic stability of the time-periodic solution.