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    题名: 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)
    作者: 黃金龍
    HUANG, JIN-LON
    贡献者: 李明融
    黃金龍
    HUANG JIN-LON
    关键词: 爆破率
    爆破常數
    爆破時間
    日期: 2002
    上传时间: 2016-03-31 16:39:18 (UTC+8)
    摘要: 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
    參考文獻: 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.
    描述: 碩士
    國立政治大學
    應用數學系
    88751010
    資料來源: http://thesis.lib.nccu.edu.tw/record/#B2002000060
    数据类型: thesis
    显示于类别:[應用數學系] 學位論文

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