Existence, uniqueness and stability of pyramidal traveling fronts in reaction-diffusion systems

Zhi Cheng Wang, Wan Tong Li, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


In the one-dimensional space, traveling wave solutions of parabolic differential equations have been widely studied and well characterized. Recently, the mathematical study on higher-dimensional traveling fronts has attracted a lot of attention and many new types of nonplanar traveling waves have been observed for scalar reaction-diffusion equations with various nonlinearities. In this paper, by using the comparison argument and constructing appropriate super- and subsolutions, we study the existence, uniqueness and stability of threedimensional traveling fronts of pyramidal shape for monotone bistable systems of reaction-diffusion equations in R3. The pyramidal traveling fronts are characterized as either a combination of planar traveling fronts on the lateral surfaces or a combination of two-dimensional V-form waves on the edges of the pyramid. In particular, our results are applicable to some important models in biology, such as Lotka-Volterra competition-diffusion systems with or without spatio-temporal delays, and reaction-diffusion systems of multiple obligate mutualists.

Original languageEnglish (US)
Pages (from-to)1-40
Number of pages40
JournalScience China Mathematics
StateAccepted/In press - Aug 3 2016


  • bistability
  • existence
  • pyramidal traveling fronts
  • reaction-diffusion systems
  • stability
  • uniqueness

ASJC Scopus subject areas

  • Mathematics(all)


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