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dc.contributor.advisorGomes, Diogo A.
dc.contributor.authorMachado Velho, Roberto
dc.date.accessioned2017-09-11T12:50:16Z
dc.date.available2017-09-11T12:50:16Z
dc.date.issued2017-09-10
dc.identifier.citationMachado Velho, R. (2017). Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods. KAUST Research Repository. https://doi.org/10.25781/KAUST-602L9
dc.identifier.doi10.25781/KAUST-602L9
dc.identifier.urihttp://hdl.handle.net/10754/625444
dc.description.abstractIn this dissertation, we present two research projects, namely finite-state mean-field games and the Hughes model for the motion of crowds. In the first part, we describe finite-state mean-field games and some applications to socio-economic sciences. Examples include paradigm shifts in the scientific community and the consumer choice behavior in a free market. The corresponding finite-state mean-field game models are hyperbolic systems of partial differential equations, for which we propose and validate a new numerical method. Next, we consider the dual formulation to two-state mean-field games, and we discuss numerical methods for these problems. We then depict different computational experiments, exhibiting a variety of behaviors, including shock formation, lack of invertibility, and monotonicity loss. We conclude the first part of this dissertation with an investigation of the shock structure for two-state problems. In the second part, we consider a model for the movement of crowds proposed by R. Hughes in [56] and describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an Eikonal equation with Dirichlet or Neumann data. We first establish a priori estimates for the solutions. Next, we consider radial solutions, and we identify a shock formation mechanism. Subsequently, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. We also propose a new numerical method for the solution of Fokker-Planck equations and then to systems of PDEs composed by a Fokker-Planck equation and a potential type equation. Finally, we illustrate the use of the numerical method both to the Hughes model and mean-field games. We also depict cases such as the evacuation of a room and the movement of persons around Kaaba (Saudi Arabia).
dc.language.isoen
dc.subjectMean-field games
dc.subjectCrowd motion
dc.subjectFokker-Planck Equation
dc.subjectNumerical Methods
dc.subjectHamilton-Jacobi equations
dc.titleFinite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods
dc.typeDissertation
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
thesis.degree.grantorKing Abdullah University of Science and Technology
dc.contributor.committeememberTempone, Raul
dc.contributor.committeememberSun, Shuyu
dc.contributor.committeememberFalcone, Maurizio
thesis.degree.disciplineApplied Mathematics and Computational Science
thesis.degree.nameDoctor of Philosophy
refterms.dateFOA2018-06-14T02:28:52Z


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