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| 研究生： |
林俊宏 Lin, Jiunn-Hon |
|---|---|
| 論文名稱： |
關於非線性微分方程的正則性 The Regularity of Solutions for Non-linear Differential Equation u'' - u^p = 0 |
| 指導教授： |
李明融
Li, Meng-Rong |
| 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： | 43 |
| 中文關鍵詞： | 微分方程 、正則性 、爆破 、爆破速率 |
| 外文關鍵詞： | differential equation, regularity, blow-up, blow-up rate |
| 相關次數： | 點閱：73 下載：0 |
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本研究中討論了非線性微分方程式之解的正則性。在這之中發現了一些有趣的現象，得到了方程式解可以做任意次的微分，並且得到對該解任意次微分後其值趨近到無限大時之爆破速率、爆破常數及當其值遞減至零時的爆破速率、爆破常數。
In this paper we work with the regularity of solutions for the non-linear ordinary differential equation u''-u^p=0 for some well-defined functions u^p. We have found some interesting phenomena, u belongs to C^q for any q in positive integer, blow-up constant, blow-up rate, null point and decay rate of u^(n) are obtained in this work, through that we get the characterization for these equations in this case.
Introduction.
Chapter 0 The Calligraphy Equation.
Chapter I The Equation u''-u^p=0, p belogns to positive integer.
Chapter II The Equation u''-u^p=0, p belongs to rational number.
Chapter III The Blow-up Rate and Blow-up Constant.
Appendix Proof of Theorem 5.
[1].Bellman. R. Stability Theory Of Differential Equation.McGraw-Hill Book Company. 1953.
[2].Li, M. R. Nichtlineare Wellengleichungen 2. Ordnung auf beschraenkten Gebieten. PhD-Dissertation Tuebingen 1994.
[3].Li, M. R. Estimation for The Life-span of solutions forSemi-linear Wave Equations. Proceedings of the Workshop on Differential Equations V. Jan.10-11,1997, National Tsing-hua Uni. Hsinchu, Taiwan.
[4].Li, M. R. On the Differential Equation u''=u^p, Preprint, 1998.
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