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

Said Boulite; S. Hadd; L. Maniar

doi:10.3934/dcdsb.2005.5.265

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2005, Volume 5, Issue 2: 265-276. Doi: 10.3934/dcdsb.2005.5.265

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

1.
Department of Mathematics, Semlalia Faculty of Sciences, Cadi Ayyad University, P.O. 2390, 40001 Marrakesh
2.
Department of Mathematics, Cadi Ayyad University, Faculty of Sciences Semlalia, B.P. 2390, Marrakesh
3.
Department of Mathematics, Cadi Ayyad University, Faculty of Sciences Semlalia, B.P. 2390, Marrakesh, 40000

Received: April 30, 2001

Revised: January 31, 2003

Published: April 2008

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Abstract

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:

C0-semigroups,
Hille-Yosida operators,
critical spectrum,
Dyson-Phillips series,
unbounded perturbations and dynamical population equations.

Mathematics Subject Classification: 34K05, 34K20, 47D06.

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