### 抄録

The initial-boundary value problems and the corresponding stationary problems of the discrete Boltzmann equation are studied. It is shown that stationary solutions exist for any boundary data. These stationary solutions are unique in a neighborhood of a given constant Maxwellian. Furthermore, it is proved that if both initial and boundary data are close to a given constant Maxwellian, then unique solutions to the initial-boundary value problems exist globally in time and converge to the corresponding unique stationary solutions exponentially as time goes to infinity. The stability condition plays an essential role in proving the uniqueness and the time-asymptotic stability results.

元の言語 | English |
---|---|

ページ（範囲） | 389-429 |

ページ数 | 41 |

ジャーナル | Japan Journal of Industrial and Applied Mathematics |

巻 | 8 |

発行部数 | 3 |

DOI | |

出版物ステータス | Published - 1991 10 1 |

外部発表 | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)
- Applied Mathematics

### これを引用

**Existence and stability of stationary solutions to the discrete Boltzmann equation.** / Kawashima, Shuichi.

研究成果: Article

}

TY - JOUR

T1 - Existence and stability of stationary solutions to the discrete Boltzmann equation

AU - Kawashima, Shuichi

PY - 1991/10/1

Y1 - 1991/10/1

N2 - The initial-boundary value problems and the corresponding stationary problems of the discrete Boltzmann equation are studied. It is shown that stationary solutions exist for any boundary data. These stationary solutions are unique in a neighborhood of a given constant Maxwellian. Furthermore, it is proved that if both initial and boundary data are close to a given constant Maxwellian, then unique solutions to the initial-boundary value problems exist globally in time and converge to the corresponding unique stationary solutions exponentially as time goes to infinity. The stability condition plays an essential role in proving the uniqueness and the time-asymptotic stability results.

AB - The initial-boundary value problems and the corresponding stationary problems of the discrete Boltzmann equation are studied. It is shown that stationary solutions exist for any boundary data. These stationary solutions are unique in a neighborhood of a given constant Maxwellian. Furthermore, it is proved that if both initial and boundary data are close to a given constant Maxwellian, then unique solutions to the initial-boundary value problems exist globally in time and converge to the corresponding unique stationary solutions exponentially as time goes to infinity. The stability condition plays an essential role in proving the uniqueness and the time-asymptotic stability results.

KW - discrete Boltzmann equation

KW - stationary solution

KW - time-asymptotic stability

KW - time-global solution

KW - uniqueness

UR - http://www.scopus.com/inward/record.url?scp=0000494406&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000494406&partnerID=8YFLogxK

U2 - 10.1007/BF03167144

DO - 10.1007/BF03167144

M3 - Article

AN - SCOPUS:0000494406

VL - 8

SP - 389

EP - 429

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 3

ER -