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| Title: | 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) |
| Authors: | 黃金龍
HUANG, JIN-LON |
| Contributors: | 李明融
黃金龍
HUANG JIN-LON |
| Keywords: | 爆破率
爆破常數
爆破時間 |
| Date: | 2002 |
| Issue Date: | 2016-03-31 16:39:18 (UTC+8) |
| Abstract: | 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 uo,u1,c2 > 0-----19
5.1.2 Blows up Phenomena for u` under uo,u1,c2 > 0-----19
5.1.3 Blows up Phenomena for u"" under uo,u1,c1,c2 > 0-----19
5.2 Properties of Blow-up Constant and Coefficients-----19
5.2.1 The Case of 1 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 5.3.2 The Case of q=2-----25
References-----26 |
| Reference: | 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. |
| Description: | 碩士
國立政治大學
應用數學系
88751010 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#B2002000060 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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