On the stability of travelling wave solutions of a one-dimensional model system for compressible viscous gas

Akitaka Matsumura, Kenji Nishihara

Research output: Contribution to journalArticle

179 Citations (Scopus)

Abstract

Travelling wave solutions with shock profile for a one-dimensional model system associated with compressible viscous gas are investigated in terms of asymptotic stability. The travelling wave solution is proved to be asymptotically stable, provided the initial disturbance is suitably small and of zero constant component. The proof is given by the elemental L2 energy method.

Original languageEnglish
Pages (from-to)17-25
Number of pages9
JournalJapan Journal of Applied Mathematics
Volume2
Issue number1
DOIs
Publication statusPublished - 1985 Jun
Externally publishedYes

Fingerprint

One-dimensional Model
Traveling Wave Solutions
Energy Method
Asymptotic stability
Asymptotically Stable
Gases
Asymptotic Stability
Shock
Disturbance
Zero
Gas
Profile

Keywords

  • asymptotic stability
  • Cauchy problem
  • compressible viscous gas
  • travelling wave solutions

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

Cite this

On the stability of travelling wave solutions of a one-dimensional model system for compressible viscous gas. / Matsumura, Akitaka; Nishihara, Kenji.

In: Japan Journal of Applied Mathematics, Vol. 2, No. 1, 06.1985, p. 17-25.

Research output: Contribution to journalArticle

@article{292348e2cce941e9af4a0106e54b52d4,
title = "On the stability of travelling wave solutions of a one-dimensional model system for compressible viscous gas",
abstract = "Travelling wave solutions with shock profile for a one-dimensional model system associated with compressible viscous gas are investigated in terms of asymptotic stability. The travelling wave solution is proved to be asymptotically stable, provided the initial disturbance is suitably small and of zero constant component. The proof is given by the elemental L2 energy method.",
keywords = "asymptotic stability, Cauchy problem, compressible viscous gas, travelling wave solutions",
author = "Akitaka Matsumura and Kenji Nishihara",
year = "1985",
month = "6",
doi = "10.1007/BF03167036",
language = "English",
volume = "2",
pages = "17--25",
journal = "Japan Journal of Industrial and Applied Mathematics",
issn = "0916-7005",
publisher = "Springer Japan",
number = "1",

}

TY - JOUR

T1 - On the stability of travelling wave solutions of a one-dimensional model system for compressible viscous gas

AU - Matsumura, Akitaka

AU - Nishihara, Kenji

PY - 1985/6

Y1 - 1985/6

N2 - Travelling wave solutions with shock profile for a one-dimensional model system associated with compressible viscous gas are investigated in terms of asymptotic stability. The travelling wave solution is proved to be asymptotically stable, provided the initial disturbance is suitably small and of zero constant component. The proof is given by the elemental L2 energy method.

AB - Travelling wave solutions with shock profile for a one-dimensional model system associated with compressible viscous gas are investigated in terms of asymptotic stability. The travelling wave solution is proved to be asymptotically stable, provided the initial disturbance is suitably small and of zero constant component. The proof is given by the elemental L2 energy method.

KW - asymptotic stability

KW - Cauchy problem

KW - compressible viscous gas

KW - travelling wave solutions

UR - http://www.scopus.com/inward/record.url?scp=0001923997&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001923997&partnerID=8YFLogxK

U2 - 10.1007/BF03167036

DO - 10.1007/BF03167036

M3 - Article

AN - SCOPUS:0001923997

VL - 2

SP - 17

EP - 25

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 1

ER -