Asymptotic Behavior For Some Nonlocal Dispersal Equations

This paper is concerned with the asymptotic behavior for some nonlocal dispersal equations.We consider the different asymptotical stability of the solution of the spatially degenerate nonlocal dispersal Logistic equations and the solution of reaction diffusion equations,and the stability of the unique positive constant solution of the nonlocal ratio-dependent prey-predator modelIn the second part,we consider the different asymptotical stability of the solution of the spatially degenerate nonlocal dispersal Logistic equations and the solution of reaction diffusion equations.We find that the effect of degeneracy on its nonlocal problem very different to the effects of the classical reaction-diffusion equationsThirdly,we consider the stability of the unique positive constant solution of the nonlocal ratio-dependent prey-predator model.We use the sub-super solutions method to show the asymptotical behavior of the solution of the nonlocal dispersal equations.