Persistence and failure of complete spreading in delayed reaction-diffusion equations

Guo Lin, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


This paper deals with the long time behavior in terms of complete spreading for a population model described by a reaction-diffusion equationwith delay, of which the corresponding reaction equation is bistable. When a complete spreading occurs in the corresponding undelayed equation with initial value admitting compact support, it is proved that the invasion can also be successful in the delayed equation if the time delay is small. To spur on a complete spreading, the choice of the initial value would be very technical due to the combination of delay and Allee effects. In addition, we show the possible failure of complete spreading in a quasimonotone delayed equation to illustrate the complexity of the problem.

Original languageEnglish (US)
Pages (from-to)1059-1072
Number of pages14
JournalProceedings of the American Mathematical Society
Issue number3
StatePublished - Mar 2016

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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