## 抄録

The asymptotic stability of traveling wave solutions with shock profile is considered for scalar viscous conservation laws u_{t}+f(u)_{x}=μu_{xx} with the initial data u_{0} which tend to the constant states u_{±} as x→±∞. Stability theorems are obtained in the absence of the convexity of f and in the allowance of s (shock speed)=f′(u_{±}). Moreover, the rate of asymptotics in time is investigated. For the case f′(u_{+})<s<f′(u_{-}), if the integral of the initial disturbance over (-∞, x) is small and decays at the algebraic rate as |x|→∞, then the solution approaches the traveling wave at the corresponding rate as t→∞. This rate seems to be almost optimal compared with the rate in the case f=u^{2}/2 for which an explicit form of the solution exists. The rate is also obtained in the case f′(u_{±}=s under some additional conditions. Proofs are given by applying an elementary weighted energy method to the integrated equation of the original one. The selection of the weight plays a crucial role in those procedures.

本文言語 | English |
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ページ（範囲） | 83-96 |

ページ数 | 14 |

ジャーナル | Communications in Mathematical Physics |

巻 | 165 |

号 | 1 |

DOI | |

出版ステータス | Published - 1994 10月 |

## ASJC Scopus subject areas

- 統計物理学および非線形物理学
- 物理学および天文学（全般）
- 数理物理学