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dc.contributor.authorHaskovec, Jen
dc.contributor.authorKreusser, Lisaen
dc.contributor.authorMarkowich, Pen
dc.date.accessioned2019-11-01T00:30:56Z
dc.date.available2019-11-01T00:30:56Z
dc.date.issued2019-01-01en
dc.identifier.issn1539-6746
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/298300
dc.description.abstractWe study the global existence of solutions of a discrete (ODE-based) model on a graph describing the formation of biological transportation networks, introduced by Hu and Cai. We propose an adaptation of this model so that a macroscopic (PDE-based) system can be obtained as its formal continuum limit. We prove the global existence of weak solutions of the macroscopic PDE model. Finally, we present results of numerical simulations of the discrete model, illustrating the convergence to steady states, their non-uniqueness as well as their dependence on initial data and model parameters.
dc.publisherInternational Press of Boston, Inc.
dc.rightsAll rights reserved
dc.titleODE-and PDE-based modeling of biological transportation networksen
dc.typeArticle
prism.endingPage1256
prism.issueIdentifier5en
prism.publicationDate2019en
prism.publicationNameCommunications in Mathematical Sciencesen
prism.startingPage1235
prism.volume17en
dc.identifier.doi10.17863/CAM.45355
dcterms.dateAccepted2019-05-04en
rioxxterms.versionofrecord10.4310/CMS.2019.v17.n5.a4en
rioxxterms.versionAM
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2019-01-01en
dc.contributor.orcidKreusser, Lisa [0000-0002-1131-1125]
dc.identifier.eissn1945-0796
rioxxterms.typeJournal Article/Reviewen
cam.orpheus.successThu Jan 30 10:36:18 GMT 2020 - Embargo updated*
rioxxterms.freetoread.startdate2019-01-01


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