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

Akitaka Matsumura; Kenji Nishihara

doi:10.1007/BF03167036

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 journal › Article › peer-review

186 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 language	English
Pages (from-to)	17-25
Number of pages	9
Journal	Japan Journal of Applied Mathematics
Volume	2
Issue number	1
DOIs	https://doi.org/10.1007/BF03167036
Publication status	Published - 1985 Jun
Externally published	Yes

Keywords

asymptotic stability
Cauchy problem
compressible viscous gas
travelling wave solutions

ASJC Scopus subject areas

Engineering(all)
Applied Mathematics

Access to Document

10.1007/BF03167036

Fingerprint Dive into the research topics of 'On the stability of travelling wave solutions of a one-dimensional model system for compressible viscous gas'. Together they form a unique fingerprint.

Cite this

@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 = jun,

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 -