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Authoritative: http://dx.doi.org/10.1016/j.physa.2004.02.056   (Publisher's PDF... likely be available here.)

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Abstract

We consider a model introduced recently [Nature 424(2003)900], for describing competition between two languages, which in typical situations predicts the extinction of one of them. We generalize it by introducing a spatial dependence in terms of a reaction-diffusion equation. We show that in this generalized model both languages can survive, each mostly concentrated in a different geographical area.

Keywords: Reaction-diffusion equations; Language competition

@article{patriarca04languageCompetition,
  author={Marco Patriarca and Teemu Leppanen},
  title={Modeling language competition},
  journal={Physica A: Statistical Mechanics and its Applications},
  year={2004},
  month={July},
  volume={338},
  number={1-2},
  pages={296-299},
  doi={10.1016/j.physa.2004.02.056},
  url={http://www.isrl.uiuc.edu/~amag/langev/paper/patriarca04languageCompetition.html},
  keywords={Reaction-diffusion equations; Language competition}
}