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研究生: 王志揚
Wang, Zhi-Yang
論文名稱: 線性熱方程,雙曲型p方程組,和黏滯性p方程組之解的比較
Comparison of Solutions for the Linear Heat Equation, Hyperbolic p-System, and Viscous p-System
指導教授: 連文璟
Lien, Wen-Ching
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系應用數學碩博士班
Department of Mathematics
論文出版年: 2005
畢業學年度: 93
語文別: 英文
論文頁數: 25
中文關鍵詞: 正則性長時間行為遞減速度
外文關鍵詞: decay rate, regularity, large-time behavior
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  •   這篇論文中我們將要比較下列三個方程式:線性熱方程,雙曲型p方程組,和黏滯性p方程組。我們討論的重點在於這些方程式之解的基本性質,特別是其正則性,長時間行為,以及遞減速度。除此之外,我們也重新整理解釋與這三個方程相關的一些重要結果。

     In this paper we will compare the following three partial differential equations: the linear heat equation, hyperbolic p-system and viscous p-system. The main point of the argument lies in the fundamental properties of solutions for these equations, especially their regularity, large-time behaviors and decay rates. In addition, we also review and interpret some important results related to the three equations.

    Contents 1 Introduction......................3 2 Heat equation.....................5 2.1 Existence of solution for the initial value problem.................................5 2.2 L^p-L^q estimate....................7 3 Hyperbolic p-system..................11 4 Green's function for the linear viscous p-system....................................13 References................................21 A Fourier transform method.............22 B Shock and rarefaction waves..........23

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