Global existence of solutions for a nonlinear size-structured population model with distributed delay in the recruitment

Abstract

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 a Banach space by using the 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 Banach spaces, while the global existence of solution is obtained by the estimates of the solution and the extension theorem.