Free Boundary Problems Of Leslie-Gower Predator-Prey Model And Nonlocal Fisher-KPP Model With Shifting Environments

In this thesis,we mainly study the long time dynamical behavior of the LeslieGower prey-predator model with two free boundaries in some shifting environments and the free boundary problems of Fisher-KPP model with nonlocal diffusion term in a shifting environment.The first chapter is mainly reviewed the background and current status of the research problem.Then we introduce the main work in this article and the significance of the research.In Chapter 2,we consider the following Leslie-Gower predator-prey problem with two free boundaries in some shifting environments （?） where d_i,μ_i（i=1,2）,α,β,h₀ and g₀ are positive constants,h（t）,g（t）is the moving boundary to be determined.The functions A₁（ξ）and A₂（ζ）are assumed to be Lipschitz continuous,strictly increasing on[-l0,0]and satisfied （?） where l₀>0,a_0,1,a_0,2<0 and a₁,a₂>0 are constants.The initial functions u₀（x）and v₀（x）satisfy （?） Firstly,we obtain the spreading-vanishing-borderline spreading trichotomy by some comparison principles.Secondly,we discuss the effect of changes in parameters on the dynamic behavior of species at long time by changing a parameter in the model.In Chapter 3,we study the free boundary problem of a Fisher-KPP model with nonlocal diffusion term in a shifting environment （?） where A（ξ）satisfies the same assumption as A₁（ξ）and A₂（ξ）,and（?） where l₀>0,a₀<0 and a>0 are constants.The initial functions u₀（x）satisfies （?） We assume that the kernel function J:R→R is continuous,nonnegative and satisfies （J）J（0）>0,∫R J（x）dx=1,J is symmetric,supR J<∞.The model describes the evolution of the species when initially occupy the bounded region[0,h₀].We establish the long-time dynamical behavior,including spreadingvanishing dichotomy.