Population density functions: a differential equation approach.

@article{Nairn1988PopulationDF,
  title={Population density functions: a differential equation approach.},
  author={Angus Nairn and G J O'neill},
  journal={Journal of regional science},
  year={1988},
  volume={28 1},
  pages={89-102}
}
"This paper introduces a new mathematical technique to describe population density functions. Two length scales, which characterize the variation of these density functions within a region, are identified. A differential equation is derived and asymptotic solutions obtained. Two specific techniques, the method of matched asymptotic expansions and the method of multiple scales, are introduced and illustrated by application to population densities at both the metropolitan and regional levels." 

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