Reaction-diffusion equations of two species competing for two complementary resources with internal storage

Sze Bi Hsu, Jifa Jiang*, Feng Bin Wang

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

5 Scopus citations

Abstract

This paper examines a system of reaction-diffusion equations arising from a mathematical model of two microbial species competing for two complementary resources with internal storage in an unstirred chemostat. The governing system can be reduced to a limiting system based on two uncoupled conservation principles. One of main technical difficulties in our analysis is the singularities in the reaction terms. Conditions for persistence of one population and coexistence of two competing populations are derived from eigenvalue problems, maximum principle and the theory of monotone dynamical systems.

Original languageEnglish
Pages (from-to)918-940
Number of pages23
JournalJournal of Differential Equations
Volume251
Issue number4-5
DOIs
StatePublished - 15 08 2011
Externally publishedYes

Keywords

  • Coexistence
  • Complementary resources
  • Internal storage
  • Maximum principle
  • Monotone dynamical systems
  • Unstirred chemostat

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