A note on the stability of the rarefaction wave of the Burgers equation

Youichi Hattori, Kenji Nishihara

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    43 Citations (Scopus)


    This paper is concerned with the asymptotic behavior toward the rarefaction wave uR(x/t) of the solution of the Burgers equation with viscosity. If the initial data are suitably close to constant state u± at x=±∞, then the solution u(x, t), roughly speaking, satisfies supR |u -uR| ∼t-1/2 as t → ∞ and, except for the "neighborhoods" of the corners, x=u±t of uR, sup |u-uR|∼t-1. In the proof the exact forms of u are available.

    Original languageEnglish
    Pages (from-to)85-96
    Number of pages12
    JournalJapan Journal of Industrial and Applied Mathematics
    Issue number1
    Publication statusPublished - 1991 Feb



    • asymptotic behavior
    • Hopf transformation
    • rarefaction wave

    ASJC Scopus subject areas

    • Applied Mathematics
    • Engineering(all)

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