Propagation Dynamics Of A Time Periodic Integrodifference Equation Of Second Order

In this thesis,propagation dynamics of a time periodic integrodifference e-quation of second order is considered.We mainly study the speed of asymptotic spread in case of the initial value of equation is compactly supported,the existence of nonconstant periodic traveling wave solutions,the minimal wave speed of trav-eling wave solutions,and the accelerated propagation phenomenon in case of the initial value of equation is slowly decay.The equation does not generate mono-tone semiflow and can not be studied by constructing two monotone governing equations with the same propagation thresholdFirstly,we discuss the speed of asymptotic spread of the solution when the initial value is compactly supported.We construct an auxiliary monotone equa-tion of first order according to the periodicity and non-negative property of the growth function.The speed of asymptotic spread of the solution is obtained by constructing monotone function and using the spreading theory of monotone e-quationsIn addition,we consider the minimal wave speed traveling wave solutions for the equation of second order.A multi-step operator is defined according to the periodicity of the equation,and the fixed point theorem is used for the opera-tor.We transform the existence of traveling wave solutions to the existence of generalized upper and lower solutions,and then obtain the existence of traveling wave solutions by constructing proper upper and lower solutions.When the wave speed equals to the speed of asymptotic spreading,we obtain the existence of the traveling wave solutions by passing to a limit.When the wave speed is less than the speed of spreading,we obtain the nonexistence of traveling wave solutions by contradiction.Here,the minimal wave speed of the traveling wave solutions equals to the speed of asymptotic spread of the solution in the case of initial value is compactly supportedFinally,we discuss the phenomenon of accelerated propagation of solutions in the case of initial value is slowly decay.Phenomenon of accelerated propagation is that the level set of solutions moves faster and faster when time approaches infinity.Firstly,we get that the level set of the solution is non-empty based on the continuity of the solution.Then,we prove that the speed of spreading is greater than any given number by constructing the monotone function and utilizing the comparison principle.That means the phenomenon of accelerated propagation of solutions.Furthermore,when the initial value satisfies certain assumptions,it is proved that the level set of the solution can be estimated from the initial value of slowly decay by constructing proper upper solution.