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Title:	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
Authors:	林俊宏 Lin, Jiunn-Hon
Contributors:	李明融 Li, Meng-Rong 林俊宏 Lin, Jiunn-Hon
Keywords:	微分方程正則性爆破爆破速率 differential equation regularity blow-up blow-up rate
Date:	1998
Issue Date:	2016-04-27 11:15:03 (UTC+8)
Abstract:	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.
Reference:	[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.
Description:	碩士國立政治大學應用數學系 86751012
Source URI:	http://thesis.lib.nccu.edu.tw/record/#B2002001689
Data Type:	thesis
Appears in Collections:	[應用數學系] 學位論文

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