### Abstract

This paper is concerned with the asymptotic behavior toward the rarefaction wave of the solution of a one-dimensional barotropic model system for compressible viscous gas. We assume that the initial data tend to constant states at x=±∞, respectively, and the Riemann problem for the corresponding hyperbolic system admits a weak continuous rarefaction wave. If the adiabatic constant γ satisfies 1≦γ≦2, then the solution is proved to tend to the rarefaction wave as t→∞ under no smallness conditions of both the difference of asymptotic values at x=±∞ and the initial data. The proof is given by an elementary L^{2}-energy method.

Original language | English |
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Pages (from-to) | 325-335 |

Number of pages | 11 |

Journal | Communications in Mathematical Physics |

Volume | 144 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1992 Feb |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*144*(2), 325-335. https://doi.org/10.1007/BF02101095

**Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas.** / Matsumura, Akitaka; Nishihara, Kenji.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 144, no. 2, pp. 325-335. https://doi.org/10.1007/BF02101095

}

TY - JOUR

T1 - Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas

AU - Matsumura, Akitaka

AU - Nishihara, Kenji

PY - 1992/2

Y1 - 1992/2

N2 - This paper is concerned with the asymptotic behavior toward the rarefaction wave of the solution of a one-dimensional barotropic model system for compressible viscous gas. We assume that the initial data tend to constant states at x=±∞, respectively, and the Riemann problem for the corresponding hyperbolic system admits a weak continuous rarefaction wave. If the adiabatic constant γ satisfies 1≦γ≦2, then the solution is proved to tend to the rarefaction wave as t→∞ under no smallness conditions of both the difference of asymptotic values at x=±∞ and the initial data. The proof is given by an elementary L2-energy method.

AB - This paper is concerned with the asymptotic behavior toward the rarefaction wave of the solution of a one-dimensional barotropic model system for compressible viscous gas. We assume that the initial data tend to constant states at x=±∞, respectively, and the Riemann problem for the corresponding hyperbolic system admits a weak continuous rarefaction wave. If the adiabatic constant γ satisfies 1≦γ≦2, then the solution is proved to tend to the rarefaction wave as t→∞ under no smallness conditions of both the difference of asymptotic values at x=±∞ and the initial data. The proof is given by an elementary L2-energy method.

UR - http://www.scopus.com/inward/record.url?scp=34249841641&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249841641&partnerID=8YFLogxK

U2 - 10.1007/BF02101095

DO - 10.1007/BF02101095

M3 - Article

AN - SCOPUS:34249841641

VL - 144

SP - 325

EP - 335

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -