Existence Of Traveling Wave Solutions Of A Nonlocal Diffusive Competition System Of Three Species With Delays

This thesis is composed of three chapters.In the first chapter,we mainly introduce the relative backgrounds and problems of reaction diffusion equations,including the concepts of traveling wave solutions and traveling front solutions.Moreover,we deeply summarize the relative research on the traveling wave solutions and traveling front solutions of competitive diffusion systems of three species.In the end,we introduce the quasi-monotonicity condition and the week quasi-monotonicity condition.In the second chapter,we consider the existence of traveling wave solution of the following nonlocal competitive diffusion system with delays,which connects(?)In fact,by changing the above system into a cooperative system,we now consider traveling wave solutions connecting(0,0,0)and(1,1,1).Then the cooperative nonlocal diffusion system changes into a differential integrate system following the transform of traveling wave solution.Next,we verify the quasi-monotonicity condition and construct the super-sub solutions.In the end,we obtain the existence of traveling wave solutions by using of the method of super-sub solutions and fixed point theorem.Based on the second chapter,we further consider the existence of traveling wave solution of the following nonlocal competitive diffusion system with delays(?)The existence of delays(?),makes the system more complex.By directly computing,for sufficiently small (?),we have verified the week quasi-monotonicity condition andthe super-sub solutions in the second chapter are also the super-sub solutions of the new cooperative system.In the end,similar to the proof in the second chapter,we have proved that for sufficiently small (?),there exist traveling wave solutions connecting(0,0,0)and(1,1,1).