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題名 有非線性干擾的二階微分方程
作者 林修竹
貢獻者 李明融
林修竹
關鍵詞 blow up
life-span
日期 2003
上傳時間 17-九月-2009 13:44:31 (UTC+8)
摘要 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.
參考文獻 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.
描述 碩士
國立政治大學
應用數學研究所
88751012
92
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0088751012
資料類型 thesis
dc.contributor.advisor 李明融zh_TW
dc.contributor.author (作者) 林修竹zh_TW
dc.creator (作者) 林修竹zh_TW
dc.date (日期) 2003en_US
dc.date.accessioned 17-九月-2009 13:44:31 (UTC+8)-
dc.date.available 17-九月-2009 13:44:31 (UTC+8)-
dc.date.issued (上傳時間) 17-九月-2009 13:44:31 (UTC+8)-
dc.identifier (其他 識別碼) G0088751012en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/32555-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學研究所zh_TW
dc.description (描述) 88751012zh_TW
dc.description (描述) 92zh_TW
dc.description.abstract (摘要) 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 (摘要) 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 (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0088751012en_US
dc.subject (關鍵詞) blow upen_US
dc.subject (關鍵詞) life-spanen_US
dc.title (題名) 有非線性干擾的二階微分方程zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Meng-Rong Li, On the Differential Equation u``-u^p=0, Preprint, National Chengchi University, 1999.zh_TW
dc.relation.reference (參考文獻) I-Chen Chen, Some Studies in Differential Equation}, Preprint, National Chengchi University, 1999.zh_TW
dc.relation.reference (參考文獻) C.Corduneanu, Principle of Differential and Integral Equations, Allyn and Bacon,Inc., Boston, 1971.zh_TW
dc.relation.reference (參考文獻) D.W. Jordan and P.Smith, Nonlinear Ordinary Differential Equations, Clarendon Press, Oxford, 1977.zh_TW