Differentiability of the age-dependent population system with time delay in the birth process

In this paper, by using semigroup approach, we concerned with the regularity of the age-dependent population system with instantaneous time delay in the birth process. We prove that, under some additional condition, the solution semigroup {T(t),t⩾0} of the population evolution equation is eventually differentiable, i.e., there exists t0>0 such that T(t) is differentiable for t>t0.