On the asymptotic behavior of a size-structured model arising in population dynamics

Size-structured model arising in population dynamics

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DOI:

https://doi.org/10.26637/mjm11S/007

Abstract

We study the asymptotic behavior of a semilinear size-structured population model with delay when the nonlinearity is small in some sense. The novelty in this work is that the operator governing the linear part of the equation does not generate a compact semigroup unlike in the results present in literature. In such a case the spectrum does not consist wholly of eigenvalues but also has a non-trivial component called Browder’s essential spectrum. To overcome the lack of compactness, we give a localization of Browder’s essential spectrum of the operator governing the linear part and we use the Perron-Frobenius spectral analysis adapted to semigroups of positive operators in Banach lattices to investigate the long time behavior of the system.

Keywords:

Perron-Frobenius, positive operators, structured population models, Browder’s essential spectrum, asymptotic behavior, semigroups of operators

Mathematics Subject Classification:

35B40, 35R10, 47D06
  • Nadia Drisi Université Cadi Ayyad, Faculté des Sciences Semlalia, Département de Mathématiques, B.P. 2390, Marrakesh, Morocco,
  • Brahim Es-sebbar Université Cadi Ayyad, Faculté des Sciences et Techniques Guéliz, Département de Mathématiques, B.P. 549, Marrakesh, Morocco
  • Ezzinbi Khalil Université Cadi Ayyad, Faculté des Sciences Semlalia, Département de Mathématiques, B.P. 2390, Marrakesh, Morocco,
  • Samir Fatajou Université Cadi Ayyad, Faculté des Sciences Semlalia, Département de Mathématiques, B.P. 2390, Marrakesh, Morocco,
  • Pages: 92-114
  • Date Published: 01-10-2023
  • Vol. 11 No. S (2023): Malaya Journal of Matematik (MJM): Special Issue Dedicated to Professor Gaston M. N'Guérékata’s 70th Birthday

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01-10-2023

How to Cite

Nadia Drisi, Brahim Es-sebbar, E. Khalil, and Samir Fatajou. “On the Asymptotic Behavior of a Size-Structured Model Arising in Population Dynamics: Size-Structured Model Arising in Population Dynamics”. Malaya Journal of Matematik, vol. 11, no. S, Oct. 2023, pp. 92-114, doi:10.26637/mjm11S/007.

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Vol. 11 No. S (2023): Malaya Journal of Matematik (MJM): Special Issue Dedicated to Professor Gaston M. N'Guérékata’s 70th Birthday

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Copyright (c) 2023 Nadia Drisi, Brahim Es-sebbar, Ezzinbi Khalil, Samir Fatajou

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