Measure Solutions for Some Models in Population Dynamics

@article{Caizo2013MeasureSF,
  title={Measure Solutions for Some Models in Population Dynamics},
  author={Jos{\'e} A. Ca{\~n}izo and Jos{\'e} A. Carrillo and S{\'i}lvia Cuadrado},
  journal={Acta Applicandae Mathematicae},
  year={2013},
  volume={123},
  pages={141-156}
}
We give a direct proof of well-posedness of solutions to general selection-mutation and structured population models with measures as initial data. This is motivated by the fact that some stationary states of these models are measures and not L1 functions, so the measures are a more natural space to study their dynamics. Our techniques are based on distances between measures appearing in optimal transport and common arguments involving Picard iterations. These tools provide a simplification of… CONTINUE READING

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