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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/86784


    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 16:43:12 (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.
    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.
    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:[Department of Mathematical Sciences] Theses

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