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姓名 鄭淞方(Song-Fang Cheng)  查詢紙本館藏   畢業系所 數學系
論文名稱 非線性二階常微方程組兩點邊界值問題之解的存在性與唯一性
(The Existence and Uniqueness of Solutions for a Two Point Boundary Value Problem of Nonlinear System of Ordinary Differential Equations.)
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摘要(中) 論文摘要
我們的論文主題是要證明某些非線性二階常微方程組兩點邊界值問題之解的存在性與唯一性。證明的原理主要是推廣C.Dafermos的方法到具有源項的方程組。我們的做法主要是建立在解的自相似性上,並利用此性質把原系統化成一個二階常微分方程組。我們假設所有可能的解是一致有界的情況下,我們使用Leray-Shauder定理來建立解的存在性。最後我們使用Gronwall 不等式性質來建立解的唯一性。
摘要(英) Abstract
We prove the existence and uniqueness of solution for a two-point boundary value problem of some nonlinear system of second order ordinary differential equations. The nonlinear system comes from the reduction of a nonlinear balance laws with viscosity under the assumption that the solution is self-similar. We construct the solution by Leray-Schauder fixed point theorem under the assumption that all possible solutions have an uniform bound. Moreover, by provide the estimate of the gradient of solution, and using the Gronwall inequality, we establish the uniqueness of solution.
關鍵字(中) ★ 兩點邊界值問題
★ 自相似性
關鍵字(英) ★ limiting viscosity method
★ two point boundary value problem
論文目次 Content
Introduction.........................................1
? Existence of Riemann-Dafermos Solutions..............4
? Uniqueness of Riemann-Dafermos Solutions............12
? Reference...........................................17
參考文獻 References
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指導教授 洪盟凱(John M. Hong) 審核日期 2006-6-23
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