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dc.contributor.authorSantambrogio, Filippo
dc.contributor.authorRoudneff-Chupin, Aude
dc.contributor.authorMaury, Bertrand
dc.subjectContinuity Equationen
dc.subjectCrowd Motionen
dc.subjectGradient Flowen
dc.subjectWasserstein Distanceen
dc.titleA macroscopic crowd motion model of gradient flow typeen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenA simple model to handle the flow of people in emergency evacuation situations is considered: at every point x, the velocity U(x) that individuals at x would like to realize is given. Yet, the incompressibility constraint prevents this velocity field to be realized and the actual velocity is the projection of the desired one onto the set of admissible velocities. Instead of looking at a microscopic setting (where individuals are represented by rigid discs), here the macroscopic approach is investigated, where the unknwon is the evolution of the density . If a gradient structure is given, say U is the opposite of the gradient of D where D is, for instance, the distance to the exit door, the problem is presented as a Gradient Flow in the Wasserstein space of probability measures. The functional which gives the Gradient Flow is neither finitely valued (since it takes into account the constraints on the density), nor geodesically convex, which requires for an ad-hoc study of the convergence of a discrete scheme.en
dc.relation.isversionofjnlnameMathematical Models and Methods in Applied Sciences
dc.relation.isversionofjnlpublisherWorld Scientificen

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