Asymptotic behavior for scalar viscous conservation laws with boundary effect

Tai Ping Liu, Kenji Nishihara

    Research output: Contribution to journalArticle

    54 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)296-320
    Number of pages25
    JournalJournal of Differential Equations
    Volume133
    Issue number2
    Publication statusPublished - 1997 Jan 20

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    Viscous Conservation Laws
    Boundary Effect
    Scalar Conservation Laws
    Asymptotic stability
    Shock waves
    Shock
    Conservation
    Boundary layers
    Asymptotic Behavior
    Boundary Value
    Shock Waves
    Asymptotic Stability
    Half-space
    Boundary Layer

    ASJC Scopus subject areas

    • Analysis

    Cite this

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

    In: Journal of Differential Equations, Vol. 133, No. 2, 20.01.1997, p. 296-320.

    Research output: Contribution to journalArticle

    Liu, Tai Ping ; Nishihara, Kenji. / Asymptotic behavior for scalar viscous conservation laws with boundary effect. In: Journal of Differential Equations. 1997 ; Vol. 133, No. 2. pp. 296-320.
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