### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 761-790 |

Number of pages | 30 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 44 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2012 |

### Fingerprint

### Keywords

- Asymptotic behavior
- Bohm criterion
- Convergence rate
- Sheath
- Stationary solution
- Weighted energy method

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics
- Computational Mathematics

### Cite this

*SIAM Journal on Mathematical Analysis*,

*44*(2), 761-790. https://doi.org/10.1137/110835657

**Asymptotic stability of boundary layers to the Euler-poisson equations arising in plasma physics.** / Nishibata, Shinya; Ohnawa, Masashi; Suzuki, Masahiro.

Research output: Contribution to journal › Article

*SIAM Journal on Mathematical Analysis*, vol. 44, no. 2, pp. 761-790. https://doi.org/10.1137/110835657

}

TY - JOUR

T1 - Asymptotic stability of boundary layers to the Euler-poisson equations arising in plasma physics

AU - Nishibata, Shinya

AU - Ohnawa, Masashi

AU - Suzuki, Masahiro

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Asymptotic behavior

KW - Bohm criterion

KW - Convergence rate

KW - Sheath

KW - Stationary solution

KW - Weighted energy method

UR - http://www.scopus.com/inward/record.url?scp=84861391105&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861391105&partnerID=8YFLogxK

U2 - 10.1137/110835657

DO - 10.1137/110835657

M3 - Article

AN - SCOPUS:84861391105

VL - 44

SP - 761

EP - 790

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 2

ER -