我們研究了Lotka-Volterra類型功能反應的擴散捕食者 – 被捕食者模型的行進波解，其中兩個物種都服從羅吉斯成長，使得捕食者的攜帶能力與獵物成比例。 我們研究了連續型和離散型的行進波解。 我們的目標是看看兩個物種是否能夠最終生存下去，如果一個外來入侵的捕食者引入現有獵物的棲息地。 應用Schauder的不動點理論，借助適當的上下解，證明了該模型行進波解的存在性。 通過推導行進波的不存在性，我們也確定了該模型行進波的最小速度。

We study the traveling wave solutions of a diffusive predator-prey model of Lotka-Volterra type functional response in which both species obey the logistic growth such that the carrying capacity of the predator is proportional to the prey. Both continuous and discrete diffusion are addressed. Our aim is to see whether both species can survive eventually, if an alien invading predator is introducing to the habitat of an existing prey. Applying Schauder's fixed point theory with the help of suitable upper and lower solutions, the existence of traveling wave solutions for this model is proven. By deriving the non-existence of traveling waves, we also determine the minimal speed of traveling waves for this model.

Contents 
Chapter 1 Introduction   1 
1.1 Traveling wave solutions for a Lotka-Volterra type diffusive predator-prey model   1
1.2 Traveling wave solutions for a lattice dynamical system arising in a predator-prey model   3
Chapter 2 Traveling wave solutions for a Lotka-Volterra type diffusive predator-prey model   5
2.1 Introduction   5 
2.2 Preliminaries   7 
2.3 Upper and lower solutions of (2.1.2)   19 
2.4 Existence of traveling wave solutions for c>=c*   26
2.5 Determination of the minimal speed   28
Chapter 3 Traveling wave solutions for a lattice dynamical system arising in a predator-prey model   30 
3.1 Introduction   30 
3.2 Preliminaries   32 
3.3 Upper and lower solutions of (3.1.2)    34 
3.4 Existence of traveling wave solutions for c>=c_*  41
3.5 Determination of the minimal speed   43
Bibliography   45

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