| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 陳冠朋 | zh_TW |
| DC.creator | Kuan-peng Chen | en_US |
| dc.date.accessioned | 2008-6-20T07:39:07Z | |
| dc.date.available | 2008-6-20T07:39:07Z | |
| dc.date.issued | 2008 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=952201006 | |
| dc.contributor.department | 數學系 | zh_TW |
| DC.description | 國立中央大學 | zh_TW |
| DC.description | National Central University | en_US |
| dc.description.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。 | zh_TW |
| dc.description.abstract | 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 $1$. | en_US |
| DC.subject | 存在性 | zh_TW |
| DC.subject | 唯一性 | zh_TW |
| DC.subject | 漸近穩定性 | zh_TW |
| DC.subject | 行波解 | zh_TW |
| DC.subject | monostable | zh_TW |
| DC.subject | 下解 | zh_TW |
| DC.subject | 上解 | zh_TW |
| DC.subject | asymptotic stability | en_US |
| DC.subject | uniqueness | en_US |
| DC.subject | existence | en_US |
| DC.subject | monostable | en_US |
| DC.subject | supersolution | en_US |
| DC.subject | subsolution | en_US |
| DC.subject | traveling wave solutions | en_US |
| DC.title | 某類網格型微分方程行波解的存在性，唯一性及穩定性 | zh_TW |
| dc.language.iso | zh-TW | zh-TW |
| DC.title | Existence, Uniqueness and Asymptotic Stability of Traveling Wave Solutions for Some Lattice Differential Equations | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |