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研究生： 楊易庸
Yang, Yi-Yung
論文名稱： 耗散系統的邊界關係推導
Derivation of boundary relations for some dissipative systems
指導教授： 江金城
Jiang, Jin-Cheng
口試委員: 蔡東和
Tsai, Dong-Ho
李明憶
Lee, Ming- Yi
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2019
畢業學年度： 107
語文別： 英文
論文頁數： 36
中文關鍵詞： 邊界關係
外文關鍵詞： boundary relations
相關次數： 點閱：2  下載：0 
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    • 在這篇論文當中，我們利用傅立葉轉換以及拉普斯轉換來推導初值邊界問
    題的邊界條件關係，我們將會利用熱方程、線性化Navier-Stokes方程以及耗散波方程來將這個方法給展示出來。

    In this thesis, we discuss the the Dirichlet-Neumann relation for some initial value boundary problems for dissipative system.
    First, we exhibit the procedure of derivation of the Dirichlet-Neumann rela-tion and its usage by 1-dimensional heat equation, which rely on the standard approach, the Fourier-Laplace transform. Then we apply this idea to another two relatively complicated examples, linearized Navier-Stokes equation and dissipative wave equation.
    In background, there is basic summarization from [3] and [4] about distribution and fundamental solution. Besides, there is also some note about the Green’s function of the linearized Navier-Stokes equation, which is stemmed from Zeng’s[2].
    This thesis is a survey based on Liu’s[1].

    1. Heat Equation.................................................2 2. Linearized Navier-Stokes Equations............................4 3. Dissipative Wave Equation.....................................9 3.1 Dirichlet-Neumann relation in the Fourier-Laplace variables.......................................................10 3.2 Inverse transformation in time variable, I..................13 3.3 Inverse transformation in time variable, II.................15 3.4 Inverse transform in space variable.........................17 4. Background...................................................21 4.0.1 Distribution..............................................21 4.0.2 Fundamental solution......................................26 4.1 Green's function for Example2...............................32 4.1.1 Summarization.............................................32 4.1.2 Utilization of reference[2]...............................35 References......................................................37

    [1] Tai-Ping Liu and Shih-Hsien Yu. On boundary relation for some dissipative
    systems. Bull. Inst. Math. Acad. Sin.(NS).
    [2] Yanni Zeng. L1 asymptotic behavior of compressible, isentropic, viscous 1-d
    flow. Communications on Pure and Applied Mathematics, 47(8):1053–1082,
    1994.
    [3] Armen H Zemanian. Distribution theory and transform analysis: an introduction to generalized functions, with applications. Courier Corporation, 1987.
    [4] Michael Renardy and Robert C Rogers. An introduction to partial differential
    equations, volume 13. Springer Science & Business Media, 2006.

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