Shock waves for a model system of the radiating gas

Shuichi Kawashima*, Shinya Nishibata

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

87 Citations (Scopus)


This paper is concerned with the existence and the asymptotic stability of traveling waves for a model system derived from approximating the one-dimensional system of the radiating gas. We show the existence of smooth or discontinuous traveling waves and also prove the uniqueness of these traveling waves under the entropy condition, in the class of piecewise smooth functions with the first kind discontinuities. Furthermore, we show that the C3-smooth traveling waves are asymptotically stable and that the rate of convergence toward these waves is t-1/4, which looks optimal. The proof of stability is given by applying the standard energy method to the integrated equation of the original one.

Original languageEnglish
Pages (from-to)95-117
Number of pages23
JournalSIAM Journal on Mathematical Analysis
Issue number1
Publication statusPublished - 1998
Externally publishedYes


  • Asymptotic stability
  • Energy method
  • Radiating gas
  • Shock wave
  • Traveling wave

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


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