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Title: | 有非線性干擾的二階微分方程 |
Authors: | 林修竹 |
Contributors: | 李明融 林修竹 |
Keywords: | blow up life-span |
Date: | 2003 |
Issue Date: | 2009-09-17 13:44:31 (UTC+8) |
Description.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)。 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. |
Reference: | Meng-Rong Li, On the Differential Equation u''-u^p=0, Preprint, National Chengchi University, 1999. I-Chen Chen, Some Studies in Differential Equation}, Preprint, National Chengchi University, 1999. C.Corduneanu, Principle of Differential and Integral Equations, Allyn and Bacon,Inc., Boston, 1971. D.W. Jordan and P.Smith, Nonlinear Ordinary Differential Equations, Clarendon Press, Oxford, 1977. |
Description: | 碩士 國立政治大學 應用數學研究所 88751012 92 |
Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0088751012 |
Data Type: | thesis |
DCField | Value | Language |
---|---|---|
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.format.mimetype | application/pdf | - |
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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