研究Kamel Hamdache於1985年發表關於小初值波茲曼方程之整體解與漸進行為之論文並補充細節與修正錯誤。

We study Kamel Hamdache's paper "Existence in the Large and Asymp-
totic Behaviour for the Boltzmann Equation" by supplying more details to proofs and correcting typos.

1. Some Notations and Function spaces p.3
2. Estimation of the Collision Operator p.6
3. Global Existence and Asymptotic Behaviour p.23
References p.34

[1] Karim M. Abadir and Jan R. Magnus, "Matrix Algebra," Cambridge University Press (2005).

[2] K. Hamdache, "Existence in the large and asymptotic behaviour for the Boltzmann equation," Japan
Journal of Applied Mathematics (1985), 1-15.

[3] R. Illner and M. Shinbrot, "The Boltzmann equation: Global existence for a rare gas in an innite
vacuum," Communications in Mathematical Physics, Volume 95 (1984), 217-226.

[4] W. Rudin, "Real and complex analysis," 3rd., McGraw-Hill Book Company, New York. (1987).

[5] L. Tartar, "Some existence theorems for semilinear hyperbolic systems in one space variable," Univ.
Wisconsin, Madison.(1980).