### 抄録

We consider the asymptotic stability of viscous shock wave φ for scalar viscous conservation laws u_{t}+f(u)_{χ}=u_{χχ} on the half-space (-∞, 0) with boundary values u|_{χ=-∞}=u_{-,}u|_{χ=0}=u_{+}. Our problem is divided into three cases depending on the sign of shock speed s of the shock (u_{-,} u_{+}). When s≤0, the asymptotic state of u becomes φ(·+d(t)), where d(t) depends implicitly on the initial data u(χ, 0) and is related to the boundary layer of the solution at the boundary χ=0. The stability of this state for s<0 will be shown by applying the weighted energy method. For s=0 a conjecture on d(t) will be presented. The case s>0 is also treated.

元の言語 | English |
---|---|

ページ（範囲） | 296-320 |

ページ数 | 25 |

ジャーナル | Journal of Differential Equations |

巻 | 133 |

発行部数 | 2 |

出版物ステータス | Published - 1997 1 20 |

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### ASJC Scopus subject areas

- Analysis

### これを引用

*Journal of Differential Equations*,

*133*(2), 296-320.

**Asymptotic behavior for scalar viscous conservation laws with boundary effect.** / Liu, Tai Ping; Nishihara, Kenji.

研究成果: Article

*Journal of Differential Equations*, 巻. 133, 番号 2, pp. 296-320.

}

TY - JOUR

T1 - Asymptotic behavior for scalar viscous conservation laws with boundary effect

AU - Liu, Tai Ping

AU - Nishihara, Kenji

PY - 1997/1/20

Y1 - 1997/1/20

N2 - We consider the asymptotic stability of viscous shock wave φ for scalar viscous conservation laws ut+f(u)χ=uχχ on the half-space (-∞, 0) with boundary values u|χ=-∞=u-,u|χ=0=u+. Our problem is divided into three cases depending on the sign of shock speed s of the shock (u-, u+). When s≤0, the asymptotic state of u becomes φ(·+d(t)), where d(t) depends implicitly on the initial data u(χ, 0) and is related to the boundary layer of the solution at the boundary χ=0. The stability of this state for s<0 will be shown by applying the weighted energy method. For s=0 a conjecture on d(t) will be presented. The case s>0 is also treated.

AB - We consider the asymptotic stability of viscous shock wave φ for scalar viscous conservation laws ut+f(u)χ=uχχ on the half-space (-∞, 0) with boundary values u|χ=-∞=u-,u|χ=0=u+. Our problem is divided into three cases depending on the sign of shock speed s of the shock (u-, u+). When s≤0, the asymptotic state of u becomes φ(·+d(t)), where d(t) depends implicitly on the initial data u(χ, 0) and is related to the boundary layer of the solution at the boundary χ=0. The stability of this state for s<0 will be shown by applying the weighted energy method. For s=0 a conjecture on d(t) will be presented. The case s>0 is also treated.

UR - http://www.scopus.com/inward/record.url?scp=0031579044&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031579044&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031579044

VL - 133

SP - 296

EP - 320

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 2

ER -