Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 132, pp. 1-23.

Title: A distributional solution to a hyperbolic problem arising
       in population dynamics

Author: Irina Kmit (Ukrainian Academy of Sciences, Ukraine)

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.

Submitted September 29, 2006. Published October 09, 2007.
Math Subject Classifications: 35L50, 35B65, 35Q80, 58J47.
Key Words: Population dynamics; hyperbolic equation; integral condition;
           singular data; distributional solution.