Front-Like Entire Solutions for Monostable Reaction-Diffusion Systems

Shi Liang Wu, Haiyan Wang

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


This paper is concerned with front-like entire solutions for monostable reaction-diffusion systems with cooperative and non-cooperative nonlinearities. In the cooperative case, the existence and asymptotic behavior of spatially independent solutions (SIS) are first proved. Further, combining a SIS and traveling fronts with different wave speeds and propagation directions, the existence and various qualitative properties of entire solutions are established by using the comparison principle. In the non-cooperative case, we introduce two auxiliary cooperative systems and establish a comparison theorem for the Cauchy problems of the three systems, and then prove the existence of entire solutions via using the comparison theorem, the traveling fronts and SIS of the auxiliary systems. Our results are applied to some biological and epidemiological models. To the best of our knowledge, it is the first work to study the entire solutions of non-cooperative reaction-diffusion systems.

Original languageEnglish (US)
Pages (from-to)505-533
Number of pages29
JournalJournal of Dynamics and Differential Equations
Issue number2
StatePublished - Jun 2013


  • Cooperative system
  • Entire solution
  • Monostable nonlinearity
  • Non-cooperative system
  • Traveling wave solution

ASJC Scopus subject areas

  • Analysis


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