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研究生:陳冠朋
研究生(外文):Kuan-peng Chen
論文名稱:某類網格型微分方程行波解的存在性,唯一性及穩定性
論文名稱(外文):Existence, Uniqueness and Asymptotic Stability of Traveling Wave Solutions for Some Lattice Differential Equations
指導教授:許正雄許正雄引用關係
指導教授(外文):Cheng-hsiung Hsu
學位類別:碩士
校院名稱:國立中央大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:英文
論文頁數:30
中文關鍵詞:存在性唯一性漸近穩定性行波解monostable下解上解
外文關鍵詞:asymptotic stabilityuniquenessexistencemonostablesupersolutionsubsolutiontraveling wave solutions
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  • 下載下載:6
  • 收藏至我的研究室書目清單書目收藏:0
在這篇論文,我們考慮以下的網格型微分方程$$u''_n(t)=-g(u_n(t))+lambda f(u_n(t))+sumlimits_{Ngeq|i|geq0}d_iu_{n-i}(t)$$在$(0,infty )$而且$ninBbb Z$,$f$,$gin C^1$,$g$是非遞減函數以及$f$是非線性monostable型。根據[7]和[9]的方法,存在critical speed $c_0$,且使得所有$c>c_0>0$,我們證明存在唯一的行波解。此外,我們也研究介於$0$和$1$之間行波解的漸近穩定性。
In this thesis, we consider the following lattice differential equation $$u''_n(t)=-g(u_n(t))+lambda f(u_n(t))+sumlimits_{Ngeq|i|geq0}d_iu_{n-i}(t)$$ on $(0,infty )$ with $ ninBbb Z$, where $f,gin C^1$,$g$ is non-decreasing and $f$ is a monostable-type nonlinearity. Following the ideas of [7] and [9], we also show the existence of a critical speed $c_0>0$ such that for all $c>c_0>0$, there exists a unique traveling wave solution of the equations. Furthermore, we also study the asymptotic stability of traveling wave solutions which are bounded between $0$ and $1$.
中文摘要...............................................i
英文摘要..............................................ii
Contents.............................................iii
Abstract...............................................1
1 Introduction........................................2
2 Existence of traveling waves........................3
2.1 Construction of subsolutions......................6
2.2 Construction of supersolutions....................9
3 Uniqueness of traveling wave solutions.............12
4 The initial value problem..........................14
5 Asymptotic stability of traveling wave solutions...22
References............................................27
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