Existence Of Travelling Wave Solutions Of The Delay Reaction-Diffusion Equation

This paper is concerned with travelling wave solutions of the delay reaction-diffusion equation.In Chapter 2 and 3, wave front solutions of the delay reaction-diffusion Cui-Lawson equation and the 2-dimensional competitive Lotka-Volterra systems are obtained by constructing an upper solution and a lower solution of a second differential equation with delay.In Chapter 4, it is discussed that travelling wave solutions of the delay reaction-diffusion equations whose reaction term do not satisfy quasimonotonicity condition or weak quasimonotonicity condition. By using cross-iteration technique and the Schauder fixed point theorem, the existence theorem of travelling wave solutions of this system is established. And its application is made to the delay competitive system.