Please use this identifier to cite or link to this item: http://hdl.handle.net/1893/22958
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dc.contributor.authorCalsina, Angelen_UK
dc.contributor.authorDiekmann, Odoen_UK
dc.contributor.authorFarkas, Jozsef Zoltanen_UK
dc.date.accessioned2017-01-06T23:17:38Z-
dc.date.available2017-01-06T23:17:38Z-
dc.date.issued2016-12en_UK
dc.identifier.urihttp://hdl.handle.net/1893/22958-
dc.description.abstractIn this work first we consider a physiologically structured population model with a distributed recruitment process. That is, our model allows newly recruited individuals to enter the population at all possible individual states, in principle. The model can be naturally formulated as a first order partial integro-differential equation, and it has been studied extensively. In particular, it is well-posed on the biologically relevant state space of Lebesgue integrable functions. We also formulate a delayed integral equation (renewal equation) for the distributed birth rate of the po\-pu\-lation. We aim to illustrate the connection between the partial integro-differential and the delayed integral equation formulation of the model utilising a recent spectral theoretic result. In particular, we consider the equivalence of the steady state problems in the two different formulations, which then leads us to characterise irreducibility of the semigroup governing the linear partial integro-differential equation. Furthermore, using the method of characteristics, we investigate the connection between the time dependent problems. In particular, we prove that any (non-negative) solution of the delayed integral equation determines a (non-negative) solution of the partial differential equation and vice versa. The results obtained for the particular distributed states at birth model then lead us to present some very general results, which establish the equivalence between a general class of partial differential and delay equation, modelling physiologically structured populations.en_UK
dc.language.isoenen_UK
dc.publisherWiley-Blackwellen_UK
dc.relationCalsina A, Diekmann O & Farkas JZ (2016) Structured populations with distributed recruitment: from PDE to delay formulation. Mathematical Methods in the Applied Sciences, 39 (18), pp. 5175-5191. http://onlinelibrary.wiley.com/doi/10.1002/mma.3898/abstract; https://doi.org/10.1002/mma.3898en_UK
dc.rightsThis item has been embargoed for a period. During the embargo please use the Request a Copy feature at the foot of the Repository record to request a copy directly from the author. You can only request a copy if you wish to use this work for your own research or private study. This is the peer reviewed version of the following article: Calsina, À., Diekmann, O., and Farkas, J. Z. (2016) Structured populations with distributed recruitment: from PDE to delay formulation. Math. Meth. Appl. Sci., 39: 5175–5191. doi: , which has been published in final form at https://doi.org/10.1002/mma.3898. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.en_UK
dc.subjectPhysiologically structured populationsen_UK
dc.subjectdistributed recruitmenten_UK
dc.subjectdelay formulationen_UK
dc.subjectspectral theory of positive operatorsen_UK
dc.titleStructured populations with distributed recruitment: from PDE to delay formulationen_UK
dc.typeJournal Articleen_UK
dc.rights.embargoreason[PDE-Delay-2016Jan29-2 (1) (1).pdf] Publisher requires embargo of 12 months after formal publication.en_UK
dc.identifier.doi10.1002/mma.3898en_UK
dc.citation.jtitleMathematical Methods in the Applied Sciencesen_UK
dc.citation.issn1099-1476en_UK
dc.citation.issn0170-4214en_UK
dc.citation.volume39en_UK
dc.citation.issue18en_UK
dc.citation.spage5175en_UK
dc.citation.epage5191en_UK
dc.citation.publicationstatusPublisheden_UK
dc.citation.peerreviewedRefereeden_UK
dc.type.statusAM - Accepted Manuscripten_UK
dc.identifier.urlhttp://onlinelibrary.wiley.com/doi/10.1002/mma.3898/abstracten_UK
dc.author.emailjozsef.farkas@stir.ac.uken_UK
dc.citation.date06/03/2016en_UK
dc.contributor.affiliationUniversitat Autonoma de Barcelonaen_UK
dc.contributor.affiliationUtrecht Universityen_UK
dc.contributor.affiliationMathematicsen_UK
dc.identifier.isiWOS:000388308500006en_UK
dc.identifier.scopusid2-s2.0-84960172514en_UK
dc.identifier.wtid576505en_UK
dc.contributor.orcid0000-0002-8794-4834en_UK
dc.date.accepted2016-01-31en_UK
dcterms.dateAccepted2016-01-31en_UK
dc.date.filedepositdate2016-03-11en_UK
rioxxterms.apcnot requireden_UK
rioxxterms.typeJournal Article/Reviewen_UK
rioxxterms.versionAMen_UK
local.rioxx.authorCalsina, Angel|en_UK
local.rioxx.authorDiekmann, Odo|en_UK
local.rioxx.authorFarkas, Jozsef Zoltan|0000-0002-8794-4834en_UK
local.rioxx.projectInternal Project|University of Stirling|https://isni.org/isni/0000000122484331en_UK
local.rioxx.freetoreaddate2016-08-07en_UK
local.rioxx.licencehttp://www.rioxx.net/licenses/under-embargo-all-rights-reserved||2016-08-06en_UK
local.rioxx.licencehttp://www.rioxx.net/licenses/all-rights-reserved|2016-08-07|en_UK
local.rioxx.filenamePDE-Delay-2016Jan29-2 (1) (1).pdfen_UK
local.rioxx.filecount1en_UK
local.rioxx.source0170-4214en_UK
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