Journal of Dynamics and Differential Equations

, Volume 23, Issue 3, pp 551–571

Persistence in Forward Nonautonomous Competitive Systems of Parabolic Equations

Open AccessArticle

DOI: 10.1007/s10884-010-9181-2

Cite this article as:
Mierczyński, J. & Shen, W. J Dyn Diff Equat (2011) 23: 551. doi:10.1007/s10884-010-9181-2


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 equationSystem of parabolic equations of Kolmogorov typePrincipal spectrumForward uniform persistence

Mathematics Subject Classification (2010)

Primary: 35K45Secondary: 35B4035K5535P0537B5592D25
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© 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