Dynamic Behavior Of A Class Of Nonlocal Dispersal Equations

As we all know,nonlocal dispersal equations have been widely used to describe different dispersal phenomena in materials science,biological invasion,chemical reactions,etc.This paper mainly studies the dynamic behavior of a class of nonlo-cal dispersal equations,including the existence of positive steady-state solutions,uniqueness and the dynamic behavior of the corresponding development equation.The main content is divided into the following two parts.Firstly,a class of spatially degenerate nonlocal dispersal Logistic equations is studied.The existence of the positive solution is obtained by the sub-super solutions method,and the uniqueness and continuity of the solution when the nonlinear term meets certain conditions are proved.Since the behavior of the equation solution depends on the parameter ?,and when ??1(?0),the be-havior of the solution is very different from the corresponding reaction-diffusion equation.Therefore,we study the asymptotic behavior of the solution when the parameter ??1(?0).Secondly,the corresponding development equation is studied.The existence and uniqueness of understanding is proved by the fixed point theorem of Banach,then we give the comparison principle,and finally discuss the asymptotic stability of the solution of the equation.