Asymptotics toward the planar rarefaction wave for viscous conservation law in two space dimensions

Masataka Nishikawa, Kenji Nishihara

    Research output: Contribution to journalArticle

    27 Citations (Scopus)

    Abstract

    This paper is concerned with the asymptotic behavior of the solution toward the planar rarefaction wave r( j) connecting u+ and u- for the scalar viscous conservation law in two space dimensions. We assume that the initial data U0(X,y) tends to constant states u± as x -»±00, respectively. Then, the convergence rate to r(j) of the solution u(t,i,j/) is investigated without the smallness conditions of |+ -u-| and the initial disturbance. The proof is given by elementary Z/2-energy method.

    Original languageEnglish
    Pages (from-to)1203-1215
    Number of pages13
    JournalTransactions of the American Mathematical Society
    Volume352
    Issue number3
    Publication statusPublished - 2000

    Fingerprint

    Viscous Conservation Laws
    Rarefaction Wave
    Scalar Conservation Laws
    Energy Method
    Convergence Rate
    Conservation
    Disturbance
    Asymptotic Behavior
    Tend

    Keywords

    • L2-energy method
    • Nonlinear stable
    • Planar rarefaction wave
    • Viscous conservation law

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Asymptotics toward the planar rarefaction wave for viscous conservation law in two space dimensions. / Nishikawa, Masataka; Nishihara, Kenji.

    In: Transactions of the American Mathematical Society, Vol. 352, No. 3, 2000, p. 1203-1215.

    Research output: Contribution to journalArticle

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