Shock waves for a model system of the radiating gas

Shuichi Kawashima, Shinya Nishibata

Research output: Contribution to journalArticle

71 Citations (Scopus)

Abstract

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
Volume30
Issue number1
DOIs
Publication statusPublished - 1998 Jan 1
Externally publishedYes

Fingerprint

Shock Waves
Shock waves
Traveling Wave
Gases
Piecewise Smooth Functions
Entropy Condition
One-dimensional System
Energy Method
Asymptotically Stable
Model
Asymptotic Stability
Discontinuity
Asymptotic stability
Rate of Convergence
Uniqueness
Entropy
Gas

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

Shock waves for a model system of the radiating gas. / Kawashima, Shuichi; Nishibata, Shinya.

In: SIAM Journal on Mathematical Analysis, Vol. 30, No. 1, 01.01.1998, p. 95-117.

Research output: Contribution to journalArticle

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