| dc.contributor.advisor | 李明融 | zh_TW |
| dc.contributor.author | 林修竹 | zh_TW |
| dc.creator (Authors) | 林修竹 | zh_TW |
| dc.date (Date) | 2003 | en_US |
| dc.date.accessioned | 2009-09-17 13:44:31 (UTC+8) | - |
| dc.date.available | 2009-09-17 13:44:31 (UTC+8) | - |
| dc.date.issued (Issue Date) | 2009-09-17 13:44:31 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0088751012 | en_US |
| dc.identifier.uri (URI) | http://nccuir.lib.nccu.edu.tw/handle/140.119/32555 | - |
| dc.description (Description) | 碩士 | zh_TW |
| dc.description (Description) | 國立政治大學 | zh_TW |
| dc.description (Description) | 應用數學研究所 | zh_TW |
| dc.description (Description) | 88751012 | zh_TW |
| dc.description (Description) | 92 | zh_TW |
| dc.description.abstract (Abstract) | 在這一篇論文中我們討論的是下列這個非線性初值問題：
u''(t)=u'(t)^q(c_1+c_2u(t)^p)
u(0) = u_0; u'(0) = u_1:
我們關注於上述問題正解的一些性質。我們發現了一些爆破(Blow-up)現象，並獲得一些結果，有關爆破率(Blow-up rate)、爆破常數(Blow-up constant)以及爆破時間(Blow-up time)。 | zh_TW |
| dc.description.abstract (Abstract) | In this paper we study the following initial value problem for the nonlinear equation,
u''(t)=u'(t)^q(c_1+c_2u(t)^p)
u(0) = u_0; u'(0) = u_1:
We are interested in properties of positive solutions of the above problem.We have found blow-up phenomena and obtained some results on blowup rates, blow-up constants and life-spans. | en_US |
| dc.description.tableofcontents | Abstract ………………………………………………………………………1
中文摘要 ………………………………………………………………………2
1 Introduction ………………………………………………………………1
2 Existence and Uniqueness of Solution ………………………………3
2.1 Existence of solution………………………………………………3
2.2 Uniqueness of solution ……………………………………………6
3 Blow-up Phenomena…………………………………………………………8
3.1 Blow-up Phenomena of u……………………………………………12
3.2 Blow-up Phenomena of u' …………………………………………18
3.3 Blow-up Phenomena of u''…………………………………………20
4 Estimations for the Life-Spans………………………………………23
5 Conclusion…………………………………………………………………29
5.1 Tables of Results …………………………………………………29
5.2 Properties of Bloe-up Rates and Blow-up Constants of u…30
Appendices……………………………………………………………………31
References……………………………………………………………………33 | zh_TW |
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| dc.language.iso | en_US | - |
| dc.source.uri (Source URI) | http://thesis.lib.nccu.edu.tw/record/#G0088751012 | en_US |
| dc.subject (Keywords) | blow up | en_US |
| dc.subject (Keywords) | life-span | en_US |
| dc.title (Title) | 有非線性干擾的二階微分方程 | zh_TW |
| dc.type (Data Type) | thesis | en |
| dc.relation.reference (Reference) | Meng-Rong Li, On the Differential Equation u''-u^p=0, Preprint, National Chengchi University, 1999. | zh_TW |
| dc.relation.reference (Reference) | I-Chen Chen, Some Studies in Differential Equation}, Preprint, National Chengchi University, 1999. | zh_TW |
| dc.relation.reference (Reference) | C.Corduneanu, Principle of Differential and Integral Equations, Allyn and Bacon,Inc., Boston, 1971. | zh_TW |
| dc.relation.reference (Reference) | D.W. Jordan and P.Smith, Nonlinear Ordinary Differential Equations, Clarendon Press, Oxford, 1977. | zh_TW |
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