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研究生:魏照誠
研究生(外文):Chao-Cheng Wei
論文名稱:波茲曼方程式柔和解的存在性
論文名稱(外文):Existence result of mild solution of Boltzmann equation
指導教授:李明融李明融引用關係
學位類別:碩士
校院名稱:國立政治大學
系所名稱:應用數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2010
畢業學年度:98
語文別:英文
論文頁數:52
中文關鍵詞:波茲曼方程柔和解的存在性均勻穩定性
相關次數:
  • 被引用被引用:0
  • 點閱點閱:209
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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.

1.Introduction ............................................1
2.Basic Kinetic Theory of Gases and the Boltzmann Equation.4
3.Element Properties of the Collision Operator............15
4.Hydrodynamical Limits:Expansions and Decomposition......22
5.Solutions in a Weighted Lebesgue Space..................35
Reference.................................................44
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