Traveling Wave And The Spreading Speed Of Two Kinds Of Nonlocal Reaction-Diffusion Equations

This paper consists of three parts: In the first part,we study the spreading speed of a Lotka-Volterra diffusion competition system with nonlocal terms.By constructing upper and lower solutions and using the contraction mapping principle,the existence and uniqueness of local solutions of the system are proved.Subsequently,the global boundedness of solutions is proved by applying the continuation theorem of solutions and the method of constructing auxiliary functions.Finally,by using truncation function,translation function and some estimation methods,we demonstrate the spreading speed of solutions with nonempty compactly supported initial data.In the second part,we consider the asymptotic spreading speed of a Lotka-Volterra diffusion competition system with nonlocal delayed terms,its time delay only appears in the interspecies competition term.By constructing auxiliary non-delayed equations,the speed of spreading is established.In the third part,we consider the existence of traveling wave solutions for reactiondiffusion equations with nonlocal delays.For two special kinds of kernel functions,we establish the relationship between the reaction-diffusion equation without nonlocal delay and the corresponding reaction-diffusion equation with nonlocal delay by using linear chain techniques and geometric singular perturbation theory.It is proved that when traveling wave solutions of reaction-diffusion equations without nonlocal delay exist,the traveling wave solutions of reaction-diffusion equations with nonlocal delay also exist under the condition that the delay is sufficiently small.