Abstract
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 L 1 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 previous approaches and are applicable or adaptable to a wide variety of models in population dynamics.
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The authors were partially supported by the Ministerio de Ciencia e Innovación, grant MTM2011-27739-C04-02, and by the Agència de Gestió d’Ajuts Universitaris i de Recerca-Generalitat de Catalunya, grant 2009-SGR-345.
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Cañizo, J.A., Carrillo, J.A. & Cuadrado, S. Measure Solutions for Some Models in Population Dynamics. Acta Appl Math 123, 141–156 (2013). https://doi.org/10.1007/s10440-012-9758-3
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DOI: https://doi.org/10.1007/s10440-012-9758-3