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Acta Applicandae Mathematicae

, Volume 123, Issue 1, pp 141–156 | Cite as

Measure Solutions for Some Models in Population Dynamics

  • José A. Cañizo
  • José A. Carrillo
  • Sílvia Cuadrado
Article

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.

Keywords

Population dynamics Selection-mutation Measure solutions Transport distances 

Mathematics Subject Classification

35Q92 92D15 92D25 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • José A. Cañizo
    • 1
  • José A. Carrillo
    • 1
    • 2
    • 3
  • Sílvia Cuadrado
    • 1
  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBarcelonaSpain
  2. 2.Department of MathematicsImperial College LondonLondonUK
  3. 3.ICREABarcelonaSpain

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