Measure solutions for some models in population dynamics

José A. Cañizo, José A. Carrillo, Sílvia Cuadrado

Research output: Contribution to journalArticleResearchpeer-review

27 Citations (Scopus)

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. © 2012 Springer Science+Business Media B.V.
Original languageEnglish
Pages (from-to)141-156
JournalActa Applicandae Mathematicae
Volume123
Issue number1
DOIs
Publication statusPublished - 1 Feb 2013

Keywords

  • Measure solutions
  • Population dynamics
  • Selection-mutation
  • Transport distances

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