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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series B Année : 2018

Time asymptotics of structured populations with diffusion and dynamic boundary conditions

Résumé

This work revisits and extends in various directions a work by J.Z. Farkas and P. Hinow (Math. Biosc and Eng, 8 (2011) 503-513) on structured populations models (with bounded sizes) with diffusion and generalized Wentzell boundary conditions. In particular, we provide first a self-contained L 1 generation theory making explicit the domain of the generator. By using Hopf maximum principle, we show that the semigroup is always irreducible regardless of the reproduction function. By using weak compactness arguments, we show first a stability result of the essential type and then deduce that the semigroup has a spectral gap and consequently the asynchronous exponential growth property. Finally, we show how to extend this theory to models with arbitrary sizes and point out an open problem pertaining to this extension.
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Dates et versions

hal-03881400 , version 1 (01-12-2022)

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Mustapha Mokhtar-Kharroubi, Quentin Richard. Time asymptotics of structured populations with diffusion and dynamic boundary conditions. Discrete and Continuous Dynamical Systems - Series B, 2018, 23 (10), pp.4087-4116. ⟨10.3934/dcdsb.2018127⟩. ⟨hal-03881400⟩
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