Eventual compactness for semiflows generated by nonlinear age-structured models

P. Magal; H. R. Thieme

doi:10.3934/cpaa.2004.3.695

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2004, Volume 3, Issue 4: 695-727. Doi: 10.3934/cpaa.2004.3.695

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Eventual compactness for semiflows generated by nonlinear age-structured models

P. Magal^1, and
H. R. Thieme^2,

1.
Department of Mathematics, Université du Havre, 76058 Le Havre
2.
Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804

Received: October 31, 2003

Revised: May 31, 2004

Published: November 2004

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Abstract

In this paper we investigate compactness properties for a semiflow generated by a semi-linear equation with non-dense domain. We start with the non-homogeneous linear case, and we derive some abstract conditions for non-autonomous semilinear equations. Then we investigate a special situation which is well adapted for age-structured equations. We conclude the paper by applying the abstract results to an age-structured model with an additional structure.

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Mathematics Subject Classification: 34Gxx, 47H20, 47J35, 58D25, 92D25.

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