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- Title
TIME ASYMPTOTICS OF STRUCTURED POPULATIONS WITH DIFFUSION AND DYNAMIC BOUNDARY CONDITIONS.
- Authors
Mokhtar-Kharroubi, Mustapha; Richard, Quentin
- Abstract
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 L1 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.
- Subjects
BOUNDARY value problems; H-spaces; HOPF algebras; DIFFERENTIAL equations; NUMERICAL analysis; PARTIAL differential equations
- Publication
Discrete & Continuous Dynamical Systems - Series B, 2018, Vol 23, Issue 10, p4087
- ISSN
1531-3492
- Publication type
Article
- DOI
10.3934/dcdsb.2018127