A distributional solution to a hyperbolic problem arising in population dynamics

Abstract

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 D'-solution in the framework of intrinsic multiplication of distributions. We also investigate the regularity of this solution.

Keywords

• Population dynamics
• hyperbolic equation
• integral condition
• singular data
• distributional solution