Advection-mediated competition in general environments

King Yeung Lam, Wei Ming Ni

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We consider a reaction-diffusion-advection system of two competing species with one of the species dispersing by random diffusion as well as a biased movement upward along resource gradient, while the other species by random diffusion only. It has been shown that, under some non-degeneracy conditions on the environment function, the two species always coexist when the advection is strong. In this paper, we show that for general smooth environment function, in contrast to what is known, there can be competitive exclusion when the advection is strong, and, we give a sharp criterion for coexistence that includes all previously considered cases. Moreover, when the domain is one-dimensional, we derive in the strong advection limit a system of two equations defined on different domains. Uniqueness of steady states of this non-standard system is obtained when one of the diffusion rates is large.

Original languageEnglish (US)
Pages (from-to)3466-3500
Number of pages35
JournalJournal of Differential Equations
Issue number9
StatePublished - Nov 1 2014

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc.


  • Advection
  • Competition exclusion
  • Dispersal
  • Monotone dynamical system
  • Reaction-diffusion


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