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.