Global Existence of Solution for a Nonlinear Size-structured Population Model with Distributed Delay in the Recruitment

In this paper we study a nonlinear size-structured population model with distributed delay in the recruitment. The delayed problem is reduced into an abstract initial value problem of an ordinary differential equation in the Banach space by using the delay semigroup techniques. The local existence and uniqueness of solution as well as the continuous dependence on initial conditions are obtained by using the general theory of quasi-linear evolution equations in nonreflexive Banach spaces, while the global existence of solution is obtained by the estimates of the solution and the extension theorem.