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Mathematics > Analysis of PDEs

arXiv:2201.05323 (math)
[Submitted on 14 Jan 2022 (v1), last revised 31 May 2022 (this version, v2)]

Title:Modelling physiologically structured populations: renewal equations and partial differential equations

Authors:Eugenia Franco, Odo Diekmann, Mats Gyllenberg
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Abstract:We analyse the long term behaviour of the measure-valued solutions of a class of linear renewal equations modelling physiologically structured populations. The renewal equations that we consider are characterised by a regularisation property of the kernel. This regularisation property allows to deduce the large time behaviour of the measure-valued solutions from the asymptotic behaviour of their absolutely continuous, with respect to the Lebesgue measure, component. We apply the results to a model of cell growth and fission and to a model of waning and boosting of immunity. For both models we relate the renewal equation (RE) to the partial differential equation (PDE) formulation and draw conclusions about the asymptotic behaviour of the solutions of the PDEs.
Subjects: Analysis of PDEs (math.AP); Dynamical Systems (math.DS)
MSC classes: 92D25, 45M05, 45D05, 45A05
Cite as: arXiv:2201.05323 [math.AP]
  (or arXiv:2201.05323v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2201.05323

Submission history

From: Eugenia Franco [view email]
[v1] Fri, 14 Jan 2022 07:11:12 UTC (62 KB)
[v2] Tue, 31 May 2022 08:13:26 UTC (62 KB)
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