Electron. J. Diff. Eqns., Vol. 2007(2007), No. 132, pp. 1-23.

A distributional solution to a hyperbolic problem arising in population dynamics

Irina Kmit

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 9, 2007.
Math Subject Classifications: 35L50, 35B65, 35Q80, 58J47.
Key Words: Population dynamics; hyperbolic equation; integral condition; singular data; distributional solution.

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Irina Kmit
Institute for Applied Problems of Mechanics and Mathematics
Ukrainian Academy of Sciences
Naukova St. 3b, 79060 Lviv, Ukraine
email: kmit@informatik.hu-berlin.de

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