Asymptotic behavior of solutions to the system of compressible adiabatic flow through porous media

Kenji Nishihara, Masataka Nishikawa

    Research output: Contribution to journalArticle

    13 Citations (Scopus)


    Hsiao and Serre in [Chinese Ann. Math. Ser. B, 16B (1995), pp. 1-14] showed the solution to the system {vt - ux = 0, (t,x) ∈ R+ × R, ut + p(v,s)x = -αu, α > 0, st = 0 with initial data (v,u,s)(0,x) = (vo, uo, so) (x) → (v, u±, s) as x → ±∞ tends to the following nonlinear parabolic equation time-asymptotically: {v̄t = -1/αp(v̄,so)xx, (t,x) ∈ R+ × R, ū = 1/αp(v̄,so)x. In this paper we find its convergence rate, which will be optimal.

    Original languageEnglish
    Pages (from-to)216-239
    Number of pages24
    JournalSIAM Journal on Mathematical Analysis
    Issue number1
    Publication statusPublished - 2001



    • Asymptotic behavior
    • Convergence rate
    • The system of compressible adiabatic flow

    ASJC Scopus subject areas

    • Mathematics(all)
    • Analysis
    • Applied Mathematics

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