### Abstract

We consider a semi-infinite expanse of a rarefied gas bounded by an infinite plane wall. The temperature of the wall is T_{0}, and the gas is initially in equilibrium with density ρ_{0} and temperature T_{0}. The temperature of the wall is suddenly changed to T_{w} at time t = 0 and is kept at Tw afterward. We study the quantitative short time behavior of the gas in response to the abrupt change of the wall temperature on the basis of the linearized Boltzmann equation. Our approach is based on a straightforward calculation of the exact formulas derived by Duhamel's integral. Our method allows us to establish the pointwise estimates of the microscopic distribution and the macroscopic variables in short time. We show that the short-time solution consists of the free molecular ow and its perturbation, which exhibits logarithmic singularities along the characteristic line and on the boundary.

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

Pages (from-to) | 765-789 |

Number of pages | 25 |

Journal | Kinetic and Related Models |

Volume | 12 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2019 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Numerical Analysis
- Modelling and Simulation

### Cite this

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*Kinetic and Related Models*, vol. 12, no. 4, pp. 765-789. https://doi.org/10.3934/krm.2019030

**Effect of abrupt change of the wall temperature in the kinetic theory.** / Kuo, Hung-Wen.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Effect of abrupt change of the wall temperature in the kinetic theory

AU - Kuo, Hung-Wen

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We consider a semi-infinite expanse of a rarefied gas bounded by an infinite plane wall. The temperature of the wall is T0, and the gas is initially in equilibrium with density ρ0 and temperature T0. The temperature of the wall is suddenly changed to Tw at time t = 0 and is kept at Tw afterward. We study the quantitative short time behavior of the gas in response to the abrupt change of the wall temperature on the basis of the linearized Boltzmann equation. Our approach is based on a straightforward calculation of the exact formulas derived by Duhamel's integral. Our method allows us to establish the pointwise estimates of the microscopic distribution and the macroscopic variables in short time. We show that the short-time solution consists of the free molecular ow and its perturbation, which exhibits logarithmic singularities along the characteristic line and on the boundary.

AB - We consider a semi-infinite expanse of a rarefied gas bounded by an infinite plane wall. The temperature of the wall is T0, and the gas is initially in equilibrium with density ρ0 and temperature T0. The temperature of the wall is suddenly changed to Tw at time t = 0 and is kept at Tw afterward. We study the quantitative short time behavior of the gas in response to the abrupt change of the wall temperature on the basis of the linearized Boltzmann equation. Our approach is based on a straightforward calculation of the exact formulas derived by Duhamel's integral. Our method allows us to establish the pointwise estimates of the microscopic distribution and the macroscopic variables in short time. We show that the short-time solution consists of the free molecular ow and its perturbation, which exhibits logarithmic singularities along the characteristic line and on the boundary.

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U2 - 10.3934/krm.2019030

DO - 10.3934/krm.2019030

M3 - Article

VL - 12

SP - 765

EP - 789

JO - Kinetic and Related Models

JF - Kinetic and Related Models

SN - 1937-5093

IS - 4

ER -