A singular limit for hyperbolic-elliptic coupled systems in radiation hydrodynamics

Shuichi Kawashima, Shinya Nishibata

    Research output: Contribution to journalArticlepeer-review

    23 Citations (Scopus)

    Abstract

    We discuss the singular limit of solutions to the initial value problem for a certain class of hyperbolic-elliptic coupled systems. A typical example of this problem appears in radiation hydrodynamics. It is shown that the singular limit problem of the hyperbolic-elliptic system corresponds to the concrete physical problem of making the Boltzmann number become infinitesimal and the Bouguer number become infinite, with their product kept constant. We show that the solution to the hyperbolic-elliptic coupled system converges to the solution of the corresponding hyperbolic-parabolic coupled system. First, the global existence is proved by the uniform estimate which is obtained through the standard energy method. Then applying the uniform estimate, we prove the convergence of the solution.

    Original languageEnglish
    Pages (from-to)567-589
    Number of pages23
    JournalIndiana University Mathematics Journal
    Volume50
    Issue number1
    Publication statusPublished - Mar 1 2001

    All Science Journal Classification (ASJC) codes

    • General Mathematics

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