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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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