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| 研究生： |
林修竹 |
|---|---|
| 論文名稱： |
有非線性干擾的二階微分方程 |
| 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： | 2004 |
| 畢業學年度： | 92 |
| 語文別： | 英文 |
| 外文關鍵詞： | blow up, life-span |
| 相關次數： | 點閱：184 下載：40 |
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在這一篇論文中我們討論的是下列這個非線性初值問題：
u''(t)=u'(t)^q(c_1+c_2u(t)^p)
u(0) = u_0; u'(0) = u_1:
我們關注於上述問題正解的一些性質。我們發現了一些爆破(Blow-up)現象，並獲得一些結果，有關爆破率(Blow-up rate)、爆破常數(Blow-up constant)以及爆破時間(Blow-up time)。
In this paper we study the following initial value problem for the nonlinear equation,
u''(t)=u'(t)^q(c_1+c_2u(t)^p)
u(0) = u_0; u'(0) = u_1:
We are interested in properties of positive solutions of the above problem.We have found blow-up phenomena and obtained some results on blowup rates, blow-up constants and life-spans.
Abstract ………………………………………………………………………1
中文摘要 ………………………………………………………………………2
1 Introduction ………………………………………………………………1
2 Existence and Uniqueness of Solution ………………………………3
2.1 Existence of solution………………………………………………3
2.2 Uniqueness of solution ……………………………………………6
3 Blow-up Phenomena…………………………………………………………8
3.1 Blow-up Phenomena of u……………………………………………12
3.2 Blow-up Phenomena of u' …………………………………………18
3.3 Blow-up Phenomena of u''…………………………………………20
4 Estimations for the Life-Spans………………………………………23
5 Conclusion…………………………………………………………………29
5.1 Tables of Results …………………………………………………29
5.2 Properties of Bloe-up Rates and Blow-up Constants of u…30
Appendices……………………………………………………………………31
References……………………………………………………………………33
Meng-Rong Li, On the Differential Equation u''-u^p=0, Preprint, National Chengchi University, 1999.
I-Chen Chen, Some Studies in Differential Equation}, Preprint, National Chengchi University, 1999.
C.Corduneanu, Principle of Differential and Integral Equations, Allyn and Bacon,Inc., Boston, 1971.
D.W. Jordan and P.Smith, Nonlinear Ordinary Differential Equations, Clarendon Press, Oxford, 1977.