Large-time behavior of solutions to an outflow problem for a shallow water model

Bongsuk Kwon, Masahiro Suzuki, Masahiro Takayama

研究成果: Article

7 引用 (Scopus)

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We investigate the existence and the time-asymptotic stability of boundary layer solutions for a one-dimensional shallow water model. Under the subsonic condition on the far-field equilibrium state, we show that there exists a one-parameter family of boundary layer solutions satisfying the outflow constant-flux boundary condition. We also show that there is a unique time-asymptotic boundary layer profile for a given initial data, and prove its stability using standard energy methods, provided that the initial perturbation is sufficiently small. Our stability result is obtained without the zero mass condition nor "artificial" condition on the profile strength. Rather the time-asymptotic profile is determined alone by the initial perturbation from the end state so that it satisfies the zero mass condition and its amplitude is appropriately small simultaneously.

元の言語English
ページ(範囲)1883-1904
ページ数22
ジャーナルJournal of Differential Equations
255
発行部数7
DOI
出版物ステータスPublished - 2013 10 1

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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