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

Youichi Hattori, Kenji Nishihara

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    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.

    元の言語English
    ページ(範囲)85-96
    ページ数12
    ジャーナルJapan Journal of Industrial and Applied Mathematics
    8
    発行部数1
    DOI
    出版物ステータスPublished - 1991 2

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    ASJC Scopus subject areas

    • Applied Mathematics
    • Engineering(all)

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