| dc.contributor.advisor | 李明融 | zh_TW |
| dc.contributor.author (Authors) | 黃金龍 | zh_TW |
| dc.contributor.author (Authors) | HUANG JIN-LON | en_US |
| dc.creator (作者) | 黃金龍 | zh_TW |
| dc.creator (作者) | HUANG, JIN-LON | en_US |
| dc.date (日期) | 2002 | en_US |
| dc.date.accessioned | 31-Mar-2016 16:39:18 (UTC+8) | - |
| dc.date.available | 31-Mar-2016 16:39:18 (UTC+8) | - |
| dc.date.issued (上傳時間) | 31-Mar-2016 16:39:18 (UTC+8) | - |
| dc.identifier (Other Identifiers) | B2002000060 | en_US |
| dc.identifier.uri (URI) | https://ah.lib.nccu.edu.tw/item?item_id=92871 | - |
| 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) | 88751010 | zh_TW |
| dc.description.abstract (摘要) | 在這一篇論文中，我們討論的是常微分方程u\" =u<sup>P</sup>(C<sub>1</sub>+C2(u`)<sup>q</sup>\")我們發現一些現象，爆破率、爆破常數、爆破時間。而且我們還發現爆破時問與係數之間的關係，我們將在之後討論。 | zh_TW |
| dc.description.abstract (摘要) | In this paper we work with the ordinary differential equation u\" = u<sup>P</sup>(C<sub>1</sub>+C2(u`)<sup>q</sup>\"). We have found some phenomena, blow-up, blow-up rate, blow-up constant, blow-up time are obtained in this work. Further, we have also found the relationship between blow-up time and blow-up coefficients, we shall detail illustrate it later. | en_US |
| dc.description.abstract (摘要) | Abstract-----i\r\n中文摘要-----ii\r\n1 Introduction-----1\r\n1.1 The Calligraphy Equation (Li,1999)-----1\r\n1.2 The Existence of Solutions-----2\r\n\r\n2 Blow-up Phenomena for 2 > q ≧1-----6\r\n2.1 Blow-up Rate and Blow-up Constant of u(t)-----10\r\n2.2 Blow-up Rate and Blow-up Constant of u`t)-----11\r\n2.3 Blow-up Rate and Blow-up Constant of u\"\"(t)-----12\r\n\r\n3 Blow-up Phenomena for q = 2-----13\r\n3.1 Blow-up Rate and Blow-up Constant of u(t)-----13\r\n3.2 Blow-up Rate and Blow-up Constant of u`(t)-----14\r\n3.3 Blow-up Rate and Blow-up Constant of u\"\"(t)-----15\r\n\r\n4 Blow-up Phenomena for q > 2-----16\r\n4.1 Blow-up Rate and Blow-up Constant of u`(t)-----17\r\n4.2 Blow-up Rate and Blow-up Constant of u\"\"{t)-----18\r\n\r\n5 Conclusions-----19\r\n5.1 Tables-----19\r\n5.1.1 Blows up Phenomena for u under uo,u1,c2 > 0-----19\r\n5.1.2 Blows up Phenomena for u` under uo,u1,c2 > 0-----19\r\n5.1.3 Blows up Phenomena for u\"\" under uo,u1,c1,c2 > 0-----19\r\n5.2 Properties of Blow-up Constant and Coefficients-----19\r\n5.2.1 The Case of 1 5.2.2 The Case of q= 2-----22\r\n5.3 Properties of Blow-up Time and Coefficients-----23\r\n5.3.1 The Case of 1 5.3.2 The Case of q=2-----25\r\n\r\nReferences-----26 | - |
| dc.description.tableofcontents | Abstract-----i\r\n中文摘要-----ii\r\n1 Introduction-----1\r\n 1.1 The Calligraphy Equation (Li,1999)-----1\r\n 1.2 The Existence of Solutions-----2\r\n\r\n2 Blow-up Phenomena for 2 > q ≧1-----6\r\n 2.1 Blow-up Rate and Blow-up Constant of u(t)-----10\r\n 2.2 Blow-up Rate and Blow-up Constant of u`t)-----11\r\n 2.3 Blow-up Rate and Blow-up Constant of u\"(t)-----12\r\n\r\n3 Blow-up Phenomena for q = 2-----13\r\n 3.1 Blow-up Rate and Blow-up Constant of u(t)-----13\r\n 3.2 Blow-up Rate and Blow-up Constant of u`(t)-----14\r\n 3.3 Blow-up Rate and Blow-up Constant of u\"(t)-----15\r\n\r\n4 Blow-up Phenomena for q > 2-----16\r\n 4.1 Blow-up Rate and Blow-up Constant of u`(t)-----17\r\n 4.2 Blow-up Rate and Blow-up Constant of u\"{t)-----18\r\n\r\n5 Conclusions-----19\r\n 5.1 Tables-----19\r\n 5.1.1 Blows up Phenomena for u under u<sub>o</sub>,u<sub>1</sub>,c<sub>2</sub> > 0-----19\r\n 5.1.2 Blows up Phenomena for u` under u<sub>o</sub>,u<sub>1</sub>,c<sub>2</sub> > 0-----19\r\n 5.1.3 Blows up Phenomena for u\" under u<sub>o</sub>,u<sub>1</sub>,c<sub>1</sub>,c<sub>2</sub> > 0-----19\r\n 5.2 Properties of Blow-up Constant and Coefficients-----19\r\n 5.2.1 The Case of 1 <q<2----- 19\r\n 5.2.2 The Case of q= 2-----22\r\n 5.3 Properties of Blow-up Time and Coefficients-----23\r\n 5.3.1 The Case of 1 <q<2-----23\r\n 5.3.2 The Case of q=2-----25\r\n\r\nReferences-----26 | zh_TW |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#B2002000060 | en_US |
| dc.subject (關鍵詞) | 爆破率 | zh_TW |
| dc.subject (關鍵詞) | 爆破常數 | zh_TW |
| dc.subject (關鍵詞) | 爆破時間 | zh_TW |
| dc.title (題名) | 有外力干擾的二階非線性微分方程 | zh_TW |
| dc.title (題名) | Nonlinear second order differential equation with force u``(t)=uP(t)(c1+c2u`(t)q) | en_US |
| dc.type (資料類型) | thesis | en_US |
| dc.relation.reference (參考文獻) | D.H. Griffel, Applied Functional Analysis, 3rd, England, Ellis Horwood, 1985, p.116.\r\nI-Chen Chen, Some Studies in Differential Equation, Preprint, National Chengchi University, 1999.\r\nJiun-Hon Lin, The Regularity of Solutions for Nonlinear Differential Equation u``-u^p=0, Preprint, National Chengchi University, 1999.\r\nMeng-Rong Li, On the Differential Equation u``-u^p=0, Preprint, National Chengchi University, 1999. | zh_TW |
