Large-Time Behavior of Solutions to Hyperbolic-Elliptic Coupled Systems

Shuichi Kawashima, Yoshiko Nikkuni, Shinya Nishibata

    Research output: Contribution to journalArticlepeer-review

    37 Citations (Scopus)

    Abstract

    We are concerned with the asymptotic behavior of a solution to the initial value problem for a system of hyperbolic conservation laws coupled with elliptic equations. This kind of problem was first considered in our previous paper. In the present paper, we generalize the previous results to a broad class of hyperbolic-elliptic coupled systems. Assuming the existence of the entropy function and the stability condition, we prove the global existence and the asymptotic decay of the solution for small initial data in a suitable Sobolev space. Then, it is shown that the solution is well approximated, for large time, by a solution to the corresponding hyperbolic-parabolic coupled system. The first result is proved by deriving a priori estimates through the standard energy method. The spectral analysis with the aid of the a priori estimate gives the second result.

    Original languageEnglish
    Pages (from-to)297-329
    Number of pages33
    JournalArchive for Rational Mechanics and Analysis
    Volume170
    Issue number4
    DOIs
    Publication statusPublished - Dec 2003

    All Science Journal Classification (ASJC) codes

    • Analysis
    • Mathematics (miscellaneous)
    • Mechanical Engineering

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