Travelling Wave Solution And The Minimal Speed For Reaction Diffusion Equations

At the present time reaction-difusion equations have attracted much increasing research at-tention for the important practical backgrounds, they are a common model in the description ofnonlinear system such as physical phenomena, chemical processes, ecological systems. In this paper,we deal with the existence of travelling wave fronts of delay lattice diferential equations, the mini-mal speed of difusion Lotka-Volterra cooperative system and the spreading speed of Lotka-Volterracompetition system with difusion.This dissertation have fve chapters.In the frst chapter, we expound the main background related to dynamical systems which isimportant in this thesis and expound the main methods and the main results.In the second chapter, we consider the existence of the travelling wave fronts of delayed latticediferential equations. We frst convert the existence of the travelling wave fronts of delayed latticediferential equations into fxed point problem for operator equations, and then by using upper-lowersolution technique and monotone iteration method, the existence result of the fxed point problemfor the operator equations is obtained. We also reduce the existence of upper-lower solution oflattice diferential equations to the existence of weak upper-lower solution. And fnally, we applyour main results to the temporally discrete Lotka-Volterra competition system with difusion anddelay.In the third chapter, we concern with the minimal speed of difusion Lotka-Volterra cooperativesystem. By constructing the absorbing area and using the manifold theory, the minimal speed oftwo dimension Lotka-Volterra cooperative system with difusion is obtained.In the fourth chapter, we consider the spreading speed of Lotka-Volterra competition systemwith difusion. By using upper-lower solution technique, comparison principle and some conclusionsof the Fisher-KPP equation, the spreading speed of two dimension Lotka-Volterra competitionsystem with difusion is obtained.In the ffth chapter, we make a summary and outlook on the contents of this dissertation.