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.
本文言語 | English |
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ページ(範囲) | 296-320 |
ページ数 | 25 |
ジャーナル | Journal of Differential Equations |
巻 | 133 |
号 | 2 |
出版ステータス | Published - 1997 1月 20 |
ASJC Scopus subject areas
- 分析