Mathematical Modeling of Two-Population Pedestrian Congestion
This seminar introduces a novel class of cross-diffusion systems for pedestrian dynamics governed by internal energy minimization under congestion.
Overview
We introduce a new class of cross-diffusion systems to model pedestrian dynamics, where the core governing principle is the minimization of internal energy under congestion. The model employs a steepest descent algorithm where the inherent dissipation is quantified by a minimal flow process used to determine the proximal work. We prove the existence and uniqueness of the model's solutions and present detailed comparisons with established cross-diffusion models based on the Wasserstein distance. While comprehensive numerical simulations are currently being processed, the talk concludes with a presentation of numerical methods for systems in some particular cases.
Presenters
Noureddine Igbida, Full Professor, Applied Mathematics, Institut de Recherche XLIM, Université de Limoges
Brief Biography
Noureddine Igbida is a Full Professor of Mathematics at the Institut de Recherche XLIM (UMR-CNRS 7252), Université de Limoges, France.
Professor Igbida obtained his Ph.D. in Mathematics from the University of Franche-Comté, Besançon, in 1997 under the supervision of Philippe Bénilan. He subsequently held postdoctoral positions in Portugal, at the Universities of Lisbon and Coimbra, before joining the University of Picardie Jules Verne, where he served as Assistant Professor (2000–2010). Since 2010, he has been a Professor at the University of Limoges, where he currently belongs to the XLIM research institute. He was promoted to the first class of professorship in 2016 and to the exceptional class (CNU 26) in 2022.
His research interests include nonlinear partial differential equations, nonlinear analysis, calculus of variations, optimization, optimal mass transport, and applications to crowd motion and image processing. He has authored around sixty papers in international peer-reviewed journals and has supervised numerous doctoral theses.
