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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: [Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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