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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 16:43:12 (UTC+8)
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.
     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.
參考文獻 [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.
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
dc.contributor.advisor 李明融zh_TW
dc.contributor.advisor Li, Meng-Rongen_US
dc.contributor.author (Authors) 林俊宏zh_TW
dc.contributor.author (Authors) Lin, Jiunn-Honen_US
dc.creator (作者) 林俊宏zh_TW
dc.creator (作者) Lin, Jiunn-Honen_US
dc.date (日期) 1998en_US
dc.date.accessioned 27-Apr-2016 16:43:12 (UTC+8)-
dc.date.available 27-Apr-2016 16:43:12 (UTC+8)-
dc.date.issued (上傳時間) 27-Apr-2016 16:43:12 (UTC+8)-
dc.identifier (Other Identifiers) B2002001689en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/86784-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學系zh_TW
dc.description (描述) 86751012zh_TW
dc.description.abstract (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。zh_TW
dc.description.abstract (摘要) 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.en_US
dc.description.abstract (摘要) 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.
-
dc.description.tableofcontents 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.
zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002001689en_US
dc.subject (關鍵詞) 微分方程zh_TW
dc.subject (關鍵詞) 正則性zh_TW
dc.subject (關鍵詞) 爆破zh_TW
dc.subject (關鍵詞) 爆破速率zh_TW
dc.subject (關鍵詞) differential equationen_US
dc.subject (關鍵詞) regularityen_US
dc.subject (關鍵詞) blow-upen_US
dc.subject (關鍵詞) blow-up rateen_US
dc.title (題名) 關於非線性微分方程的正則性zh_TW
dc.title (題名) The Regularity of Solutions for Non-linear Differential Equation u`` - u^p = 0en_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [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.
zh_TW