### 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 |

### ASJC Scopus subject areas

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

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## Cite this

Matsumura, A., & Nishihara, K. (1992). Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas.

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