Boltzmann systems for gas mixtures in 1d torus

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)415-431
Number of pages17
JournalQuarterly of Applied Mathematics
Volume75
Issue number3
DOIs
Publication statusPublished - 2017 Jan 1

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Gas Mixture
Boltzmann equation
Boltzmann Equation
Ludwig Boltzmann
Gas mixtures
Torus
Diffusion Problem
Hard Spheres
Gases
Equilibrium State
Decay Rate
Vacuum
Initial conditions
Collision
Gas

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this

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

In: Quarterly of Applied Mathematics, Vol. 75, No. 3, 01.01.2017, p. 415-431.

Research output: Contribution to journalArticle

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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.

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