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dc.contributor.authorHaskovec, Jan
dc.contributor.authorKreusser, Lisa Maria
dc.contributor.authorMarkowich, Peter A.
dc.date.accessioned2019-12-08T10:46:05Z
dc.date.available2019-04-28T13:13:48Z
dc.date.available2019-11-13T13:39:23Z
dc.date.available2019-12-08T10:46:05Z
dc.date.issued2019-12-06
dc.identifier.citationHaskovec, J., Kreusser, L. M., & Markowich, P. (2019). ODE- and PDE-based modeling of biological transportation networks. Communications in Mathematical Sciences, 17(5), 1235–1256. doi:10.4310/cms.2019.v17.n5.a4
dc.identifier.doi10.4310/cms.2019.v17.n5.a4
dc.identifier.urihttp://hdl.handle.net/10754/632527
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.description.sponsorshipLMK was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/L016516/1 and the German National Academic Foundation (Studienstiftung des Deutschen Volkes).
dc.publisherInternational Press of Boston
dc.relation.urlhttps://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0017/0005/a004/
dc.rightsArchived with thanks to Communications in Mathematical Sciences
dc.titleODE- and PDE-based modeling of biological transportation networks
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalCommunications in Mathematical Sciences
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge, United Kingdom
pubs.publication-statusPublished
dc.identifier.arxivid1805.08526
kaust.personHaskovec, Jan
kaust.personMarkowich, Peter A.
refterms.dateFOA2019-04-29T06:34:46Z
dc.date.posted2018-05-22


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