Asymptotic behavior of radially symmetric solutions for a quasilinear hyperbolic fluid model in higher dimensions

Itsuko Hashimoto, Hideo Kozono

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    1 Citation (Scopus)

    Abstract

    We consider the large time behavior of the radially symmetric solution to the equation for a quasilinear hyperbolic model in the exterior domain of a ball in general space dimensions. In the previous paper [2], we proved the asymptotic stability of the stationary wave of the Burgers equations in the same exterior domain when the solution is also radially symmetric. On the other hand, in the 1D-case, a similar asymptotic structure as above to the damped wave equation with a convection term has been established by Ueda [10] and Ueda–Kawashima [11]. Assuming a certain condition on the boundary data on the ball and the behavior at infinity of the fluid, we shall prove that the stationary wave of our quasilinear hyperbolic model is asymptotically stable. The weighted L2-energy method plays a crucial role in removing such a restriction on the sub-characteristic condition on the stationary wave.

    Original languageEnglish
    Pages (from-to)5133-5159
    Number of pages27
    JournalJournal of Differential Equations
    Volume262
    Issue number10
    DOIs
    Publication statusPublished - 2017 May 15

    Keywords

    • Asymptotic behavior
    • Damped wave equation
    • Galerkin method
    • Stationary wave

    ASJC Scopus subject areas

    • Analysis

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