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June  2007, 7(4): 735-754. doi: 10.3934/dcdsb.2007.7.735

The asymptotic behavior of a population equation with diffusion and delayed birth process

Genni Fragnelli 1, , A. Idrissi 2, and  L. Maniar 3,

1. 

Dipartimento di Ingegneria dell’Informazione, Università degli Studi di Siena, Via Roma 56, 53100 Siena, Italy
2. 

University of Cadi Ayyad, Faculty of Sciences Semlalia, B.P. 2390, Marrakesh, 40000, Morocco
3. 

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

Received  September 2005 Revised  February 2007 Published  March 2007

This paper is devoted to study the well-posedness and the asymptotic behavior of a population equation with diffusion in $L^1$. The death and birth rates depend on the age and the spatial variable. Here we allow the birth process to depend also on some modified delay. This paper is a continuation of the studies done by Nickel, Rhandi and Schnaubelt in [28][32][33] and Fragnelli, Maniar, Piazzera and Tonetto in [15][21][29][30].
Keywords: extrapolation theory, delay boundary conditions, perturbation, evolution family, backward, asymptotic behavior., essential spectrum, Population equation, Dyson-Phillips expansion, evolution semigroup, semigroup.
Mathematics Subject Classification: 34D05, 34D10, 34K30, 35F15, 47D06, 92D2.
Citation: Genni Fragnelli, A. Idrissi, L. Maniar. The asymptotic behavior of a population equation with diffusion and delayed birth process. Discrete and Continuous Dynamical Systems - B, 2007, 7 (4) : 735-754. doi: 10.3934/dcdsb.2007.7.735
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