Show simple item record

dc.contributor.authorHaskovec, Jen
dc.contributor.authorKreusser, Lisaen
dc.contributor.authorMarkowich, Pen
dc.date.accessioned2019-08-19T23:30:57Z
dc.date.available2019-08-19T23:30:57Z
dc.identifier.issn0360-5302
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/295978
dc.description.abstractMotivated by recent papers describing the formation of biological transport networks we study a discrete model proposed by Hu and Cai consisting of an energy consumption function constrained by a linear system on a graph. For the spatially two-dimensional rectangular setting we prove the rigorous continuum limit of the constrained energy functional as the number of nodes of the underlying graph tends to infinity and the edge lengths shrink to zero uniformly. The proof is based on reformulating the discrete energy functional as a sequence of integral functionals and proving their Γ-convergence towards a continuum energy functional.
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.publisherTaylor & Francis
dc.rightsAll rights reserved
dc.rights.uri
dc.titleRigorous continuum limit for the discrete network formation problemen
dc.typeArticle
prism.endingPage1185
prism.issueIdentifier11en
prism.publicationNameCommunications in Partial Differential Equationsen
prism.startingPage1159
prism.volume44en
dc.identifier.doi10.17863/CAM.43026
dcterms.dateAccepted2019-04-22en
rioxxterms.versionofrecord10.1080/03605302.2019.1612909en
rioxxterms.versionAM
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2019-04-22en
dc.contributor.orcidKreusser, Lisa [0000-0002-1131-1125]
dc.identifier.eissn1532-4133
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idEPSRC (EP/L016516/1)
cam.issuedOnline2019-05-17en
rioxxterms.freetoread.startdate2020-01-01


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record