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

Genni Fragnelli; A. Idrissi; L. Maniar

doi:10.3934/dcdsb.2007.7.735

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2007, Volume 7, Issue 4: 735-754. Doi: 10.3934/dcdsb.2007.7.735

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

1.
Dipartimento di Ingegneria dell’Informazione, Università degli Studi di Siena, Via Roma 56, 53100 Siena
2.
University of Cadi Ayyad, Faculty of Sciences Semlalia, B.P. 2390, Marrakesh, 40000
3.
Department of Mathematics, Cadi Ayyad University, Faculty of Sciences Semlalia, B.P. 2390, Marrakesh, 40000

Received: August 31, 2005

Revised: January 31, 2007

Published: October 2007

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Abstract

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].

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Mathematics Subject Classification: 34D05, 34D10, 34K30, 35F15, 47D06, 92D25.

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