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Wardrop equilibria : long-term variant, degenerate anisotropic PDEs and numerical approximations

hal.structure.identifier
dc.contributor.authorHatchi, Roméo*
dc.date.accessioned2017-11-28T14:51:53Z
dc.date.available2017-11-28T14:51:53Z
dc.date.issued2017
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17093
dc.language.isoenen
dc.subjecttraffic congestion
dc.subjectWardrop equilibrium
dc.subjectgeneralized curves
dc.subjectanisotropic and degenerate PDEs
dc.subjectaugmented Lagrangian
dc.subject.ddc515en
dc.titleWardrop equilibria : long-term variant, degenerate anisotropic PDEs and numerical approximations
dc.typeChapitre d'ouvrage
dc.description.abstractenAs shown in [15], under some structural assumptions, working on congested traffic problems in general and increasingly dense networks leads, at the limit by Γ-convergence, to continuous minimization problems posed on measures on generalized curves. Here, we show the equivalence with another problem that is the variational formulation of an anisotropic, degenerate and elliptic PDE. For particular cases, we prove a Sobolev regularity result for the minimizers of the minimization problem despite the strong degeneracy and anisotropy of the Euler-Lagrange equation of the dual. We extend the analysis of [6] to the general case. Finally, we use the method presented in [5] to make numerical simulations.
dc.identifier.citationpages257-280
dc.relation.ispartoftitleTopological Optimization and Optimal Transport
dc.relation.ispartofeditorSantambrogio, Filippo
dc.relation.ispartofeditorChampion, Thierry
dc.relation.ispartofeditorCarlier, Guillaume
dc.relation.ispartofeditorRumpf, Martin
dc.relation.ispartofeditorOudet, Édouard
dc.relation.ispartofeditorBergounioux, Maïtine
dc.relation.ispartofpublnameDe Gruyter
dc.relation.ispartofdate2017
dc.subject.ddclabelAnalyseen
dc.relation.ispartofisbn9783110430509
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2017-12-20T15:31:17Z
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