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    Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/7934


    Title: 某類網格型微分方程行波解的存在性,唯一性及穩定性;Existence, Uniqueness and Asymptotic Stability of Traveling Wave Solutions for Some Lattice Differential Equations
    Authors: 陳冠朋;Kuan-peng Chen
    Contributors: 數學研究所
    Keywords: 存在性;唯一性;漸近穩定性;行波解;monostable;下解;上解;asymptotic stability;uniqueness;existence;monostable;supersolution;subsolution;traveling wave solutions
    Date: 2008-06-14
    Issue Date: 2009-09-22 11:09:30 (UTC+8)
    Publisher: 國立中央大學圖書館
    Abstract: 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 $1$.
    Appears in Collections:[數學研究所] 博碩士論文

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