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| 研究生： |
陳怡真 Chen, Yi-Chen |
|---|---|
| 論文名稱： |
非線性微分方程之研究 Some Studies in the Nonlinear Differential Equations |
| 指導教授： |
蔡隆義
Tsai, Long-Yi |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 1999 |
| 畢業學年度： | 87 |
| 語文別： | 英文 |
| 論文頁數： | 67 |
| 中文關鍵詞： | 微分方程 、爆破 、爆破速率 、能量方法 、生成時間 |
| 外文關鍵詞： | blow-up constant, energy method, life-span time |
| 相關次數： | 點閱：116 下載：0 |
| 分享至: |
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在這篇論文中，我們討論具有初始值條件的二階微分方程 □□□□□
和系統微分方程 □□□□□等問題。
我們利用能量方法（即能量是常數的特性）來探討上述方程解之特性。例如：生成時間、爆破和爆破速率以及局部解的漸進行為。
In this paper we shall consider the initial value problem for second order differential equation of the form □□□□□
and the system □□□□□ .
We shall discuss the blow-up properties, such as the life-span, the blow-up rate and blow-up constants, and the asymptotic behavior of the global solution by using the energy method.
List of Figures
List of Tables
Introduction
Chapter1 On the Scalar Differential Equation
1.1 Fundamental Lemmas
1.2 The Asymptotic Behavior of the Global Solutions
1.3 Estimates for the Life Span of the Blow-up Solutions
1.3.1
1.3.2
1.4 Blow-up Rate and Blow-up Constant
1.5 Properties of the Life Span Time
1.5.1 The Property of
1.5.2 The Property of 9
1.5.3 The Behavior of the Blow-up Constant
Chapter 2 On The System of Differential Equations
2.1 Fundamental Lemmas
2.2 Estimates for the Life Span Time
2.3 Particular System
2.3.1 Fundamental Lemmas
2.3.2 Estimates for the Life Span Time
(I)
(II)
Chapter 3 Conclusions
3.1 The Scalar Differential Equation
3.1.1 Table
3.1.2 Examples
3.2 The System of Differential Equation
3.2.1 Table
3.3 Particular System
3.3.1 Table
3.3.2 Examples
Bibliography
Appendix
[1] D. O'Regan, Some general existence principles and results for □□□□□(0<t<1), SIAM Journal on Mathematical Analysis, 24, 648-668,(1993).
[2] J. R. Esteban and J. L. Vazquez, On the Equation of Turbulent in One-dimensional Porous Media, Nonlinear Analysis, 10, 1303-1325, (1986).
[3] Jiun-Hon Lin, The Regularity of Solutions for Non-linear Differential Equation □□□□□, Master thesis, National Chengchi University, ( 1999).
[4] Junyu Wang and Wenjie Gao, A Singular Boundary Value Problem for the One-dimensional p -Laplacian, Journal of Mathematical Analysis and Applications, 201, 851-866,(1996).
[5] L. E. Bobisub and D. O'Regan, Existence of Positive Solutions for Singular Ordinary Differential Equations with Nonlinear Boundary Conditions, Proceedings of the American Mathematical Society, 124, 2081-2087, (1996).
[6] M. A. Herrero and J. L. Vazquez, On the Propagation Properties of a Nonlinear Degenerate Parabolic Equation, Communications in Partial Differential Equations, 7, 1381-1402, (1982).
[7] Meng-Rong Li, On the Differential Equation □□□□□, Preprint, National Chengchi University, (1999).
[8] Zuodong Yang, Existence of Positive Solutions for a Class of Singular two Point Boundary Value Problems of Second Order Nonlinear Equation, Applied Mathematics and Mechanics, 17, 465-476, (1996).
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