Mathematical analysis of an abstract model and its applications to structured populations (I)

Mohamed Boulanouar

doi:10.3934/eect.2022021

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2023, Volume 12, Issue 1: 45-70. Doi: 10.3934/eect.2022021

This issue Previous Article Stability properties for a problem of light scattering in a dispersive metallic domain Next Article On the effect of perturbations in first-order optimization methods with inertia and Hessian driven damping

Mathematical analysis of an abstract model and its applications to structured populations (I)

Mohamed Boulanouar

LMCM-RSA, 22 Rue Des Canadiens, Poitiers 86000, France

To the memory of the professor Ovide Arino. He was a philanthropist and a great mathematician.

Received: September 2021

Revised: March 2022

Early access: April 2022

Published: February 2023

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Abstract

The first part of this works deals with an integro–differential operator with boundary condition related to the interior solution. We prove that the model is governed by a strongly continuous semigroup and we precise its growth inequality. In the second part of this works, we model the proliferation-quiescence phases through a system of first order equations. We also prove that the proliferation-quiescence model is governed by a strongly continuous semigroup and we precise its growth inequality. In the last part, we give some applications in Demography and Biology.

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Mathematics Subject Classification: Primary: 35B40, 47D06; Secondary: 92D25.

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Figure 1. Schematic representation of the cell transit between (P) and (Q)

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