摺積型非線性項之網格動態系統研究
No Thumbnail Available
Date
2012
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
在本篇論文中，我們研究非線性項為摺積型的網格動態系統。本論文分成兩個部份。在第一部分，我們考慮在非線性項為單穩定摺積型的網格動態系統中的行進波，我們討論行進波的漸近行為、單調性及唯一性。在第二部份中，我們考慮在非線性項為雙穩定摺積型的網格動態系統下之雙波峰全域解。我們建構三種不同類型之雙波峰全域解。在當時間趨近負無窮大時，每一種雙波峰全域解的行為近似於連接三個平衡態中的其中兩個平衡態的兩個行進波。
In this thesis, we study a lattice dynamical system with convolution type nonlinearity. This thesis is divided into two parts. In the first part, we consider traveling front solutions of a lattice dynamical system with monostable convolution type nonlinearity. We discuss the asymptotic behaviors, monotonicity and uniqueness of traveling waves. Then, in the second part, we consider two-front entire solutions of a lattice dynamical system with bistable convolution type nonlinearity. We construct three different types of two-front entire solutions. Each of these entire solutions behaves as two traveling fronts connecting two of those three equilibria as time approaches minus infinity.
In this thesis, we study a lattice dynamical system with convolution type nonlinearity. This thesis is divided into two parts. In the first part, we consider traveling front solutions of a lattice dynamical system with monostable convolution type nonlinearity. We discuss the asymptotic behaviors, monotonicity and uniqueness of traveling waves. Then, in the second part, we consider two-front entire solutions of a lattice dynamical system with bistable convolution type nonlinearity. We construct three different types of two-front entire solutions. Each of these entire solutions behaves as two traveling fronts connecting two of those three equilibria as time approaches minus infinity.
Description
Keywords
網格動態系統, 摺積型, 行進波, 全域解, lattice dynamical system, convolution type, traveling wave, entire solution