Asymptotic stability of traveling waves for scalar viscous conservation laws with non-convex nonlinearity

Akitaka Matsumura*, Kenji Nishihara

*この研究の対応する著者

    研究成果: Article査読

    120 被引用数 (Scopus)

    抄録

    The asymptotic stability of traveling wave solutions with shock profile is considered for scalar viscous conservation laws ut+f(u)x=μuxx with the initial data u0 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=u2/2 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
    ページ(範囲)83-96
    ページ数14
    ジャーナルCommunications in Mathematical Physics
    165
    1
    DOI
    出版ステータスPublished - 1994 10

    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

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