Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Boltzmann systems for gas mixtures in 1D torus


Author: Kung-Chien Wu
Journal: Quart. Appl. Math. 75 (2017), 415-431
MSC (2010): Primary 35Q20; Secondary 92C40
DOI: https://doi.org/10.1090/qam/1460
Published electronically: December 15, 2016
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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^{\infty }_{x}L^{\infty }_{\xi ,\beta }$ 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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Additional Information

Kung-Chien Wu
Affiliation: Department of Mathematics, National Cheng Kung University, 701 Tainan, Taiwan – and – National Center for Theoretical Sciences, National Taiwan University, 106, Taipei, Taiwan
Email: kcwu@mail.ncku.edu.tw; kungchienwu@gmail.com

DOI: https://doi.org/10.1090/qam/1460
Keywords: Boltzmann equation, gas mixtures, Maxwellian states
Received by editor(s): June 13, 2016
Received by editor(s) in revised form: November 2, 2016
Published electronically: December 15, 2016
Additional Notes: This work was supported by the Ministry of Science and Technology under the grant 104-2628-M-006-003-MY4 and National Center for Theoretical Sciences. Part of this work was written during a stay at Institute of Mathematics, Academia Sinica; the author thanks Tai-Ping Liu for his kind hospitality.
Article copyright: © Copyright 2016 Brown University


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