
Wardrop equilibria : long-term variant, degenerate anisotropic PDEs and numerical approximations
Hatchi, Roméo (2017), Wardrop equilibria : long-term variant, degenerate anisotropic PDEs and numerical approximations, dans Santambrogio, Filippo; Champion, Thierry; Carlier, Guillaume; Rumpf, Martin; Oudet, Édouard; Bergounioux, Maïtine, Topological Optimization and Optimal Transport, De Gruyter, p. 257-280
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Type
Chapitre d'ouvrageDate
2017Titre de l'ouvrage
Topological Optimization and Optimal TransportAuteurs de l’ouvrage
Santambrogio, Filippo; Champion, Thierry; Carlier, Guillaume; Rumpf, Martin; Oudet, Édouard; Bergounioux, MaïtineÉditeur
De Gruyter
Isbn
9783110430509
Pages
257-280
Métadonnées
Afficher la notice complèteRésumé (EN)
As 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.Mots-clés
traffic congestion; Wardrop equilibrium; generalized curves; anisotropic and degenerate PDEs; augmented LagrangianPublications associées
Affichage des éléments liés par titre et auteur.
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Hatchi, Roméo (2015) Document de travail / Working paper
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Carlier, Guillaume; Brasco, Lorenzo (2013) Article accepté pour publication ou publié
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Dubecq, Simon (2013-01) Thèse
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Carrère, Amélie (2020-06-03) Thèse
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Bonsang, Éric; Schoenmaeckers, J. (2015) Chapitre d'ouvrage