Persistence in Forward Nonautonomous Competitive Systems of Parabolic Equations
- 335 Downloads
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.
KeywordsForward 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.
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.
- 3.Cantrell R.S., Cosner C.: Spatial Ecology via Reaction–Diffusion Equations (Wiley Series in Mathematical and Computational Biology). Wiley, Chichester (2003)Google Scholar
- 7.Henry, D.: Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics, vol. 840. Springer, Berlin, New York (1981)Google Scholar
- 17.Mierczyński, J.: The principal spectrum for linear nonautonomous parabolic PDEs of second order: basic properties. In: Special issue in celebration of Jack K. Hale’s 70th birthday, Part 2 (Atlanta, GA/Lisbon, 1998). J. Differ. Equat. 168(2), 453–476 (2000)Google Scholar
- 22.Mierczyński, J., Shen, W.: Spectral theory for random and nonautonomous parabolic equations and applications. In: Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics. Chapman & Hall/CRC, Boca Raton, FL, (2008)Google Scholar
- 23.Mierczyński, J., Shen, W.: Spectral theory for forward nonautonomous parabolic equations and applications. In: International Conference on Infinite Dimensional Dynamical Systems, York University Toronto, September 24–28, 2008, dedicated to Professor George Sell on the occasion of his 70th birthday. Fields Inst. Commun.Google Scholar