TY - GEN
T1 - On the Hughes model and numerical aspects
AU - Gomes, Diogo A.
AU - Machado Velho, Roberto
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work was partially supported by KAUST baseline and start-up funds and KAUST SRI, Uncertainty Quantification Center in Computational Science and Engineering
PY - 2017/1/5
Y1 - 2017/1/5
N2 - We study a crowd model proposed by R. Hughes in [11] and we describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an eikonal equation with Dirichlet or Neumann data. First, we establish a priori estimates for the solutions. Second, we study radial solutions and identify a shock formation mechanism. Third, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. Finally, we propose a new numerical method and consider two examples.
AB - We study a crowd model proposed by R. Hughes in [11] and we describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an eikonal equation with Dirichlet or Neumann data. First, we establish a priori estimates for the solutions. Second, we study radial solutions and identify a shock formation mechanism. Third, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. Finally, we propose a new numerical method and consider two examples.
UR - http://hdl.handle.net/10754/622731
UR - http://ieeexplore.ieee.org/document/7798683/
UR - http://www.scopus.com/inward/record.url?scp=85010739226&partnerID=8YFLogxK
U2 - 10.1109/CDC.2016.7798683
DO - 10.1109/CDC.2016.7798683
M3 - Conference contribution
SN - 9781509018376
SP - 2783
EP - 2788
BT - 2016 IEEE 55th Conference on Decision and Control (CDC)
PB - Institute of Electrical and Electronics Engineers (IEEE)
ER -