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, in Santambrogio, Filippo; Champion, Thierry; Carlier, Guillaume; Rumpf, Martin; Oudet, Édouard; Bergounioux, Maïtine, Topological Optimization and Optimal Transport, De Gruyter, p. 257-280
Book titleTopological Optimization and Optimal Transport
Book authorSantambrogio, Filippo; Champion, Thierry; Carlier, Guillaume; Rumpf, Martin; Oudet, Édouard; Bergounioux, Maïtine
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Abstract (EN)As shown in , 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  to the general case. Finally, we use the method presented in  to make numerical simulations.
Subjects / Keywordstraffic congestion; Wardrop equilibrium; generalized curves; anisotropic and degenerate PDEs; augmented Lagrangian
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