Fast propagation for reaction–diffusion cooperative systems

Wen Bing Xu, Wan Tong Li, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


This paper deals with the spatial propagation for reaction–diffusion cooperative systems. It is well-known that the solution of a reaction–diffusion equation with monostable nonlinearity spreads at a finite speed when the initial condition decays to zero exponentially or faster, and propagates fast when the initial condition decays to zero more slowly than any exponentially decaying function. However, in reaction–diffusion cooperative systems, a new possibility happens in which one species propagates fast although its initial condition decays exponentially or faster. The fundamental reason is that the growth sources of one species come from the other species. Simply speaking, we find a new interesting phenomenon that the spatial propagation of one species is accelerated by the other species. This is a unique phenomenon in reaction–diffusion systems. We present a framework of fast propagation for reaction–diffusion cooperative systems.

Original languageEnglish (US)
Pages (from-to)645-670
Number of pages26
JournalJournal of Differential Equations
Issue number2
StatePublished - Jul 15 2018


  • Accelerating fronts
  • Reaction–diffusion cooperative systems
  • Spatial propagation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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