Existence and uniqueness of solutions for a diffusion model of host-parasite dynamics

Michel Langlais, Fabio Augusto Milner

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

Milner and Patton (J. Comput. Appl. Math., in press) introduced earlier a new approach to modeling host-parasite dynamics through a convection-diffusion partial differential equation, which uses the parasite density as a continuous structure variable. A motivation for the model was presented there, as well as results from numerical simulations and comparisons with those from other models. However, no proof of existence or uniqueness of solutions to the new model proposed was included there. In the present work the authors deal with the well posedness of that model and they prove existence and uniqueness of solutions, as well as establishing some asymptotic results.

Original languageEnglish (US)
Pages (from-to)463-474
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume279
Issue number2
DOIs
StatePublished - Mar 15 2003
Externally publishedYes

Keywords

  • Diffusion models
  • Existence and uniqueness
  • Host-parasite models
  • Size-structured population models

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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