我們利用Banach固定點定理證明了波茲曼方程式的柔和解在一個加權魯貝格空間上的存在性，並證明其解在如此的範數下之均勻穩定性。 關鍵詞: 波茲曼方程，馬氏分佈函數，柔和解的存在性，均勻穩定。 / In this thesis, we consider the initial-value problem for the Boltzmann equation.We prove that the existence of mild solution in the weighted Lebesgue space by using Banach's fixed point theorem, and that the uniform stability of solution with respect to the weighted norm. Key words: Boltzmann equation, Maxwellian, existence of mild solutions, uniform stability.