Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Stability estimates of the Boltzmann equation in a half space

Authors: Myeongju Chae and Seung-Yeal Ha
Journal: Quart. Appl. Math. 65 (2007), 653-682
MSC (2000): Primary 35Q35
DOI: https://doi.org/10.1090/S0033-569X-07-01060-4
Published electronically: August 24, 2007
MathSciNet review: 2370355
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Abstract: In this paper, we study the large-time behavior and the stability of continuous mild solutions to the Boltzmann equation in a half space. For this, we introduce two nonlinear functionals measuring future binary collisions and $ L^1$-distance. Through the time-decay estimates of these functionals and the pointwise estimate of the gain part of the collision operator, we show that continuous mild solutions approach to collision free flows time-asymptotically in $ L^1$, and $ L^1$-distance at time $ t$ is uniformly bounded by that of corresponding initial data, when initial datum is a small perturbation of the vacuum.

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Additional Information

Myeongju Chae
Affiliation: Department of Applied Mathematics, Hankyong National University, Ansung 456-749, Korea
Email: mchae@kias.re.kr

Seung-Yeal Ha
Affiliation: Department of Mathematics, Seoul National University, Seoul 151-747, Korea
Email: syha@math.snu.ac.kr

DOI: https://doi.org/10.1090/S0033-569X-07-01060-4
Received by editor(s): April 13, 2006
Published electronically: August 24, 2007
Dedicated: This paper is dedicated to Tai-Ping Liu on the occasion of his sixtieth birthday.
Article copyright: © Copyright 2007 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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