Journal of Dynamics and Differential Equations

, Volume 23, Issue 3, pp 551–571 | Cite as

Persistence in Forward Nonautonomous Competitive Systems of Parabolic Equations

Open Access


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 



The first-named author was supported from resources for science in years 2009–2012 as research project (grant MENII N N201 394537, Poland). The second-named author was partially supported by NSF grant DMS–0907752.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceWrocław University of TechnologyWroclawPoland
  2. 2.Department of Mathematics and StatisticsAuburn UniversityAuburnUSA

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