抄録
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.
| 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
Asymptotic behavior for scalar viscous conservation laws with boundary effect. / Liu, Tai Ping; Nishihara, Kenji.
：: Journal of Differential Equations, 巻 133, 番号 2, 20.01.1997, p. 296-320.研究成果: Article
}
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.
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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 -