Journal of Dynamics and Differential Equations

, Volume 23, Issue 3, pp 551-571

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Persistence in Forward Nonautonomous Competitive Systems of Parabolic Equations

  • Janusz MierczyńskiAffiliated withInstitute of Mathematics and Computer Science, Wrocław University of Technology Email author 
  • , Wenxian ShenAffiliated withDepartment of Mathematics and Statistics, Auburn University


In the present paper forward nonautonomous competitive systems of two parabolic second order partial differential equations are studied. The concept of forward uniform persistence for such systems is introduced. Sufficient conditions, expressed in terms of the principal spectrum, are given for those systems to be forward uniformly persistent.


Forward nonautonomous competitive system of parabolic equation System of parabolic equations of Kolmogorov type Principal spectrum Forward uniform persistence

Mathematics Subject Classification (2010)

Primary: 35K45 Secondary: 35B40 35K55 35P05 37B55 92D25