### Abstract

We study the 1D Boltzmann equation for a mixture of two gases on a torus with the initial condition of one gas near a vacuum and the other near a Maxwellian equilibrium state. An L∞_{x} L∞_{ε,β} analysis is developed to study this mass diffusion problem, which is based on the Boltzmann equation for the single species hard sphere collision in an earlier work of the author. The decay rate of the solution is algebraic for a small time region and exponential for a large time region. Moreover, the exponential rate depends on the size of the domain.

Original language | English |
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Pages (from-to) | 415-431 |

Number of pages | 17 |

Journal | Quarterly of Applied Mathematics |

Volume | 75 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2017 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Applied Mathematics

### Cite this

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*Quarterly of Applied Mathematics*, vol. 75, no. 3, pp. 415-431. https://doi.org/10.1090/qam/1460

**Boltzmann systems for gas mixtures in 1d torus.** / Wu, Kung Chien.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Boltzmann systems for gas mixtures in 1d torus

AU - Wu, Kung Chien

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We study the 1D Boltzmann equation for a mixture of two gases on a torus with the initial condition of one gas near a vacuum and the other near a Maxwellian equilibrium state. An L∞x L∞ε,β analysis is developed to study this mass diffusion problem, which is based on the Boltzmann equation for the single species hard sphere collision in an earlier work of the author. The decay rate of the solution is algebraic for a small time region and exponential for a large time region. Moreover, the exponential rate depends on the size of the domain.

AB - We study the 1D Boltzmann equation for a mixture of two gases on a torus with the initial condition of one gas near a vacuum and the other near a Maxwellian equilibrium state. An L∞x L∞ε,β analysis is developed to study this mass diffusion problem, which is based on the Boltzmann equation for the single species hard sphere collision in an earlier work of the author. The decay rate of the solution is algebraic for a small time region and exponential for a large time region. Moreover, the exponential rate depends on the size of the domain.

UR - http://www.scopus.com/inward/record.url?scp=85018277509&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85018277509&partnerID=8YFLogxK

U2 - 10.1090/qam/1460

DO - 10.1090/qam/1460

M3 - Article

AN - SCOPUS:85018277509

VL - 75

SP - 415

EP - 431

JO - Quarterly of Applied Mathematics

JF - Quarterly of Applied Mathematics

SN - 0033-569X

IS - 3

ER -