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

Masataka Nishikawa, Kenji Nishihara

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    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

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    Keywords

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

    ASJC Scopus subject areas

    • Mathematics(all)

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