Analysis and approximation of one-dimensional scalar conservation laws with general point constraints on the flux
| Autor: | Carlotta Donadello, Ulrich Razafison, Massimiliano D. Rosini, Boris Andreianov |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Université de Bourgogne (UB)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Instytut Matematyki = Institute of Mathematics [Lublin], Uniwersytet Marii Curie-Sklodowskiej = University Marii Curie-Sklodowskiej [Lublin] (UMCS), PHC Polonium No. 331460NC, INdAM–GNAMPA Project 2017 'Equazioni iperboliche con termini nonlocali: teoria e modelli'., ANR-11-JS01-0006,CoToCoLa,Thématiques actuelles en lois de conservation(2011), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Andreianov, Boris, Jeunes Chercheuses et Jeunes Chercheurs - Thématiques actuelles en lois de conservation - - CoToCoLa2011 - ANR-11-JS01-0006 - JCJC - VALID |
| Rok vydání: | 2018 |
| Předmět: |
Crowd dynamics
Mathematical optimization Fixed point arguments Discretization General Mathematics Scalar (mathematics) Finite volume approximation Nonlocal point constraint Scalar conservation law Vehicular traffics Well-posedness Mathematics (all) Applied Mathematics 01 natural sciences MSC : 35L65 90B20 65M12 76M12 NO Crowds Data acquisition [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Doors Uniqueness [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics Mathematics Conservation law Finite volume method 010102 general mathematics [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA] 010101 applied mathematics Finite volume scheme Convergence of approximations [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] |
| Zdroj: | Journal de Mathématiques Pures et Appliquées. 116:309-346 |
| ISSN: | 0021-7824 |
| Popis: | We introduce and analyze a class of models with nonlocal point constraints for traffic flow through bottlenecks, such as exits in the context of pedestrians traffic and reduction of lanes on a road under construction in vehicular traffic. Constraints are defined based on data collected from non-local in space and/or in time observations of the flow. We propose a theoretical analysis and discretization framework that permits to include different data acquisition strategies; a numerical comparison is provided. Nonlocal constraint allows to model, e.g., the irrational behavior (" panic ") near the exit observed in dense crowds and the capacity drop at tollbooth in vehicular traffic. Existence and uniqueness of solutions are shown under suitable and " easy to check " assumptions on the constraint operator. A numerical scheme for the problem, based on finite volume methods, is designed, its convergence is proved and its validation is done with an explicit solution. Numerical examples show that nonlocally constrained models are able to reproduce important features in traffic flow such as self-organization. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect