Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/86784
題名: 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
作者: 林俊宏
Lin, Jiunn-Hon
貢獻者: 李明融
Li, Meng-Rong
林俊宏
Lin, Jiunn-Hon
關鍵詞: 微分方程
正則性
爆破
爆破速率
differential equation
regularity
blow-up
blow-up rate
日期: 1998
上傳時間: 27-Apr-2016
摘要: 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.\r\nChapter 0 The Calligraphy Equation.\r\nChapter I The Equation u``-u^p=0, p belogns to positive integer.\r\nChapter II The Equation u``-u^p=0, p belongs to rational number.\r\nChapter III The Blow-up Rate and Blow-up Constant.\r\nAppendix Proof of Theorem 5.
參考文獻: [1].Bellman. R. Stability Theory Of Differential Equation.McGraw-Hill Book Company. 1953.\r\n[2].Li, M. R. Nichtlineare Wellengleichungen 2. Ordnung auf beschraenkten Gebieten. PhD-Dissertation Tuebingen 1994.\r\n[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.\r\n[4].Li, M. R. On the Differential Equation u``=u^p, Preprint, 1998.
描述: 碩士
國立政治大學
應用數學系
86751012
資料來源: http://thesis.lib.nccu.edu.tw/record/#B2002001689
資料類型: thesis
Appears in Collections:學位論文

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