On a system of reaction-diffusion equations arising from competition with internal storage in an unstirred chemostat

Sze Bi Hsu*, Jifa Jiang, Feng Bin Wang

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

48 Scopus citations

Abstract

In this paper we study a system of reaction-diffusion equations arising from competition of two microbial populations for a single-limited nutrient with internal storage in an unstirred chemostat. The conservation principle is used to reduce the dimension of the system by eliminating the equation for the nutrient. The reduced system (limiting system) generates a strongly monotone dynamical system in its feasible domain under a partial order. We construct suitable upper, lower solutions to establish the existence of positive steady-state solutions. Given the parameters of the reduced system, we answer the basic questions as to which species survives and which does not in the spatial environment and determine the global behaviors. The primary conclusion is that the survival of species depends on species's intrinsic biological characteristics, the external environment forces and the principal eigenvalues of some scalar partial differential equations. We also lift the dynamics of the limiting system to the full system.

Original languageEnglish
Pages (from-to)2470-2496
Number of pages27
JournalJournal of Differential Equations
Volume248
Issue number10
DOIs
StatePublished - 15 05 2010
Externally publishedYes

Keywords

  • Competition of algaes
  • Droop's model
  • Global stability
  • Internal storage
  • Lower solutions
  • Maximum principle
  • Monotone dynamical system
  • Unstirred chemostat
  • Upper solutions
  • Variable yield

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