Asymptotics toward the diffusion wave for a one-dimensional compressible flow through porous media

Kenji Nishihara

    研究成果: Article査読

    18 被引用数 (Scopus)

    抄録

    Consider the Cauchy problem for a one-dimensional compressible flow through porous media, vt - ux = 0, x ∈ R, t > 0, ut + p(v)x = -αu, (v, u)|t=0 = (v0, u0) (x). Hsiao and Liu showed that the solution (v, u) behaves as the diffusion wave (v̄, ū), i.e. the solution of the porous-media equation due to the Daroy law. The optimal convergence rates have been obtained by Nishihara and co-workers. When v0(x) has the same constant state at x = ±∞, the convergence rate ∥(v - v̄)(·, t)∥L∞ = O(t-1 obtained is 'optimal', since ∥v̄(·, t)∥∞ = O(t-1/2). However, this 'optimal' convergence rate is less sufficient to determine the location of the diffusion wave. Our aim in this paper is to obtain the 'truly optimal' convergence rate by choosing suitably located diffusion waves.

    本文言語English
    ページ(範囲)177-196
    ページ数20
    ジャーナルRoyal Society of Edinburgh - Proceedings A
    133
    1
    出版ステータスPublished - 2003

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

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