Decay estimates for hyperbolic balance laws

Shuichi Kawashima, Wen An Yong

    Research output: Contribution to journalArticlepeer-review

    40 Citations (Scopus)

    Abstract

    This work is concerned with time-decay properties of small-amplitude global smooth solutions to the initial value problem for hyperbolic systems of balance laws admitting an entropy and satisfying the stability condition. By using energy methods in both the physical space and the Fourier space, we obtain the optimal decay estimates of solutions and their derivatives in the L 2-norm up to order s - 1, provided that the initial data are in Hs. A key ingredient in our analysis is a time-weighted energy estimate, leading to a decay estimate for multi-dimensional problems without assuming the L1property on initial data.

    Original languageEnglish
    Pages (from-to)1-33
    Number of pages33
    JournalZeitschrift für Analysis und ihre Anwendungen
    Volume28
    Issue number1
    DOIs
    Publication statusPublished - 2009

    All Science Journal Classification (ASJC) codes

    • Analysis
    • Applied Mathematics

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