A Distributional Solution to a Hyperbolic Problem Arising in Population Dynamics

We consider a generalization of the Lotka-McKendrick problem describing the dynamics of an age-structured population with time-dependent vital rates. The generalization consists in allowing the initial and the boundary conditions to be derivatives of the Dirac measure. We construct a unique ${\text{D}}^{\mathrm{\prime }}$-solution in the framework of intrinsic multiplication of distributions. We also investigate the regularity of this solution.