Measure Solutions for Some Models in Population Dynamics

By José A. Cañizo, José Antonio Carrillo, S. Cuadrado. 2011

71 citations recorded by the source corpus.

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 previous approaches and are applicable or adaptable to a wide variety of models in population dynamics.

Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/3d269ef55857c1ef6b8e994b1dd984045f69ca3c

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In Genetics

In Modeling and Simulation

In Public Health, Environmental and Occupational Health

Citations in the corpus

Structured Populations, Cell Growth and Measure Valued Balance Laws (2012, methodology): “An alternative construction of measure-valued solutions to these models can be obtained following ideas coming from kinetic theory [14, 7] by means of a Picard-type result for evolutions in the set of measures, see [6].”