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 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.

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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