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

陳冠朋(Kuan-peng Chen)

指導教授 ： 許正雄

國立中央大學/理學院/數學系/碩士(2008年)

摘要

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。

關鍵字

存在性 ； 唯一性 ； 漸近穩定性 ； 行波解 ； monostable ； 下解 ； 上解

並列摘要

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 $1$.

並列關鍵字

asymptotic stability ； uniqueness ； existence ； monostable ； supersolution ； subsolution ； traveling wave solutions

參考文獻

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