The Study On Traveling Wave Solutions Of Two Classes Of Species Diffusion Models

With the continuous global climate change and increasingly severe industrial pollution,the environment of the ecosystem is gradually deteriorating,which leads to the gradual degradation of the species habitat or the migration of the species to new habitats.In recent years,more and more scientific researchers have paid attention to the phenomenon of habitat changes of biological populations and the impact of this phenomenon on the persistence of biological populations.Therefore,we study a class of nonlocal diffusion Fisher-KPP equation in a shifting habitat and a class of nonlocal diffusion Lotka-Volerra cooperation system in a shifting habitat.We use the upper and lower solutions combined with the method of monotone iteration and the Schauder's fixed point theorem to study the existence of forced waves of these two models.The conclusions can provide a theoretical basis for biological control and protection of species diversity.The content of this article is divided into three chapters as follows:In chapter 1,we explain the research background and significance of this article,and introduce the development history of the two classes of biological population models.In chapter 2,we consider the forced wave of a nonlocal dispersal Fisher-KPP equation in a shifting habitat with the positive intrinsic growth function.The existence of two non-trivial,bounded and nonnegative forced waves are proved by the method of monotone iteration and the Schauder's fixed point theorem,respectively.One connects monotonously minimum and maximum linearized growth rate for the shifting speed c>0,and the other connects the minimum linearized growth rate and the trivial solution 0 if c is faster than the asymptotic spreading speed c*(?),where c*(?)is determined by the nonlocal dispersal kernel,diffusion rate and the maximum linearized growth rate.In chapter 3,in order to describe the impact of the shifting habitat on the dynamic behavior of the two cooperative species,we study the nonlocal diffusion Lotka-Volerra cooperative system in which the intrinsic growth rate is a positive function related to time and space.Using the minimum positive eigenvalues of linearized system and the forced wave of the Fisher-KPP equation to construct a pair of appropriate upper and lower solutions,and then construct a profile set and define a nonlinear operator.Furthermore,the existence of forced wave for cooperative system is transformed into the existence of a fixed point for the nonlinear operator.Lastly,we prove two forced waves of cooperative system by the method of monotone iteration and Schauder's fixed point theorem.