### Abstract

We investigate the time-asymptotic behavior for rarefied gases in the spherical domain with variable boundary temperature in ℝ^{d}, d = 1, 2, 3, under the diffuse reflection boundary condition. First, we obtain an optimal convergence rate of (1 + t)^{-d} to the steady state for free molecular flow. Next, we use this to construct the steady state solution of the Boltzmann equation for sufficiently large Knudsen number and small boundary temperature variation. We also obtain an exponential convergence to the steady state for the Boltzmann equation for small perturbation.

Original language | English |
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Pages (from-to) | 421-480 |

Number of pages | 60 |

Journal | Communications in Mathematical Physics |

Volume | 328 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*328*(2), 421-480. https://doi.org/10.1007/s00220-014-2042-9

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*Communications in Mathematical Physics*, vol. 328, no. 2, pp. 421-480. https://doi.org/10.1007/s00220-014-2042-9

**Equilibrating Effects of Boundary and Collision in Rarefied Gases.** / Kuo, Hung-Wen; Liu, Tai Ping; Tsai, Li Cheng.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Equilibrating Effects of Boundary and Collision in Rarefied Gases

AU - Kuo, Hung-Wen

AU - Liu, Tai Ping

AU - Tsai, Li Cheng

PY - 2014/1/1

Y1 - 2014/1/1

N2 - We investigate the time-asymptotic behavior for rarefied gases in the spherical domain with variable boundary temperature in ℝd, d = 1, 2, 3, under the diffuse reflection boundary condition. First, we obtain an optimal convergence rate of (1 + t)-d to the steady state for free molecular flow. Next, we use this to construct the steady state solution of the Boltzmann equation for sufficiently large Knudsen number and small boundary temperature variation. We also obtain an exponential convergence to the steady state for the Boltzmann equation for small perturbation.

AB - We investigate the time-asymptotic behavior for rarefied gases in the spherical domain with variable boundary temperature in ℝd, d = 1, 2, 3, under the diffuse reflection boundary condition. First, we obtain an optimal convergence rate of (1 + t)-d to the steady state for free molecular flow. Next, we use this to construct the steady state solution of the Boltzmann equation for sufficiently large Knudsen number and small boundary temperature variation. We also obtain an exponential convergence to the steady state for the Boltzmann equation for small perturbation.

UR - http://www.scopus.com/inward/record.url?scp=84899807486&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899807486&partnerID=8YFLogxK

U2 - 10.1007/s00220-014-2042-9

DO - 10.1007/s00220-014-2042-9

M3 - Article

VL - 328

SP - 421

EP - 480

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -