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| 研究生： |
黃金龍 HUANG JIN-LON |
|---|---|
| 論文名稱： |
有外力干擾的二階非線性微分方程 Nonlinear second order differential equation with force u''(t)=uP(t)(c1+c2u'(t)q) |
| 指導教授： | 李明融 |
| 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： | 2002 |
| 畢業學年度： | 90 |
| 語文別： | 英文 |
| 論文頁數： | 26 |
| 中文關鍵詞： | 爆破率 、爆破常數 、爆破時間 |
| 相關次數： | 點閱：137 下載：44 |
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在這一篇論文中，我們討論的是常微分方程u" =u<sup>P</sup>(C<sub>1</sub>+C2(u')<sup>q</sup>")我們發現一些現象，爆破率、爆破常數、爆破時間。而且我們還發現爆破時問與係數之間的關係，我們將在之後討論。
In this paper we work with the ordinary differential equation u" = u<sup>P</sup>(C<sub>1</sub>+C2(u')<sup>q</sup>"). We have found some phenomena, blow-up, blow-up rate, blow-up constant, blow-up time are obtained in this work. Further, we have also found the relationship between blow-up time and blow-up coefficients, we shall detail illustrate it later.
Abstract-----i
中文摘要-----ii
1 Introduction-----1
1.1 The Calligraphy Equation (Li,1999)-----1
1.2 The Existence of Solutions-----2
2 Blow-up Phenomena for 2 > q ≧1-----6
2.1 Blow-up Rate and Blow-up Constant of u(t)-----10
2.2 Blow-up Rate and Blow-up Constant of u't)-----11
2.3 Blow-up Rate and Blow-up Constant of u"(t)-----12
3 Blow-up Phenomena for q = 2-----13
3.1 Blow-up Rate and Blow-up Constant of u(t)-----13
3.2 Blow-up Rate and Blow-up Constant of u'(t)-----14
3.3 Blow-up Rate and Blow-up Constant of u"(t)-----15
4 Blow-up Phenomena for q > 2-----16
4.1 Blow-up Rate and Blow-up Constant of u'(t)-----17
4.2 Blow-up Rate and Blow-up Constant of u"{t)-----18
5 Conclusions-----19
5.1 Tables-----19
5.1.1 Blows up Phenomena for u under u<sub>o</sub>,u<sub>1</sub>,c<sub>2</sub> > 0-----19
5.1.2 Blows up Phenomena for u' under u<sub>o</sub>,u<sub>1</sub>,c<sub>2</sub> > 0-----19
5.1.3 Blows up Phenomena for u" under u<sub>o</sub>,u<sub>1</sub>,c<sub>1</sub>,c<sub>2</sub> > 0-----19
5.2 Properties of Blow-up Constant and Coefficients-----19
5.2.1 The Case of 1 <q<2----- 19
5.2.2 The Case of q= 2-----22
5.3 Properties of Blow-up Time and Coefficients-----23
5.3.1 The Case of 1 <q<2-----23
5.3.2 The Case of q=2-----25
References-----26
D.H. Griffel, Applied Functional Analysis, 3rd, England, Ellis Horwood, 1985, p.116.
I-Chen Chen, Some Studies in Differential Equation, Preprint, National Chengchi University, 1999.
Jiun-Hon Lin, The Regularity of Solutions for Nonlinear Differential Equation u''-u^p=0, Preprint, National Chengchi University, 1999.
Meng-Rong Li, On the Differential Equation u''-u^p=0, Preprint, National Chengchi University, 1999.