Asymptotic stability of boundary layers to the Euler-poisson equations arising in plasma physics

Shinya Nishibata, Masashi Ohnawa, Masahiro Suzuki

研究成果: Article査読

12 被引用数 (Scopus)

抄録

The main concern of the present paper is to analyze the behavior of a boundary layer, called a sheath, which appears over a material in contact with a plasma. The well-known Bohm criterion claims the velocity of positive ions should be faster than a certain constant for the formation of a sheath. The behavior of positive ions is governed by the Euler-Poisson equations. Mathematically, the sheath is understood as a monotone stationary solution, whose existence and asymptotic stability in one-dimensional space were proved in Suzuki's previous work. However the stability was proved under the assumption stronger than the Bohm criterion. In the present paper, we refine these results by proving the stability theorem exactly under the Bohm criterion in the spatial dimension up to three. We also deal with the degenerate case in which the Bohm criterion is marginally fulfilled.

本文言語English
ページ(範囲)761-790
ページ数30
ジャーナルSIAM Journal on Mathematical Analysis
44
2
DOI
出版ステータスPublished - 2012

ASJC Scopus subject areas

  • 分析
  • 応用数学
  • 計算数学

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