Decay property of regularity-loss type and nonlinear effects for some hyperbolic-elliptic system

Takekiyo Kubo, Shuichi Kawashima

    Research output: Contribution to journalArticlepeer-review

    16 Citations (Scopus)

    Abstract

    We study the decay property of a certain nonlinear hyperbolic-elliptic system with 2mth-order elliptic part, which is a modified version of the simplest radiating gas model. It is proved that, for m ≥ 2, the system verifies a decay property of the regularity-loss type that is characterized by the parameter m. This dissipative property is very weak in the high-frequency region and causes a difficulty in showing the global existence of solutions to the nonlinear problem. By employing the time-weighted energy method together with the optimal decay for lower-order derivatives of solutions, we overcome this difficulty and establish a global existence and asymptotic decay result. Furthermore, we show that the solution approaches the nonlinear diffusion wave described by the self-similar solution of the Burgers equation as time tends to infinity.

    Original languageEnglish
    Pages (from-to)139-159
    Number of pages21
    JournalKyushu Journal of Mathematics
    Volume63
    Issue number1
    DOIs
    Publication statusPublished - Jun 19 2009

    All Science Journal Classification (ASJC) codes

    • General Mathematics

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