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May  2005, 5(2): 265-276. doi: 10.3934/dcdsb.2005.5.265

Critical spectrum and stability for population equations with diffusion in unbounded domains

Said Boulite 1, , S. Hadd 2, and  L. Maniar 3,

1. 

Department of Mathematics, Semlalia Faculty of Sciences, Cadi Ayyad University, P.O. 2390, 40001 Marrakesh, Morocco
2. 

Department of Mathematics, Cadi Ayyad University, Faculty of Sciences Semlalia, B.P. 2390, Marrakesh, Morocco
3. 

Department of Mathematics, Cadi Ayyad University, Faculty of Sciences Semlalia, B.P. 2390, Marrakesh, 40000, Morocco

Received  May 2001 Revised  February 2003 Published  February 2005

In this work we study the asymptotic behavior of the solutions of some population equations with diffusion in unbounded domains by using the notion of critical spectrum introduced recently by R. Nagel and J. Poland [9]. To do this, we extend the abstract results of Brendle-Nagel-Poland [4], concerning the persistence under perturbations of the critical spectrum of a semigroup, to Hille-Yosida operators.
Keywords: Hille-Yosida operators, unbounded perturbations and dynamical population equations., critical spectrum, Dyson-Phillips series, C0-semigroups.
Mathematics Subject Classification: 34K05, 34K20, 47D0.
Citation: Said Boulite, S. Hadd, L. Maniar. Critical spectrum and stability for population equations with diffusion in unbounded domains. Discrete and Continuous Dynamical Systems - B, 2005, 5 (2) : 265-276. doi: 10.3934/dcdsb.2005.5.265
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