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On the discretization of some nonlinear Fokker-Planck-Kolmogorov equations and applications
Multi angle
Authors : Silva Álvarez, Francisco José (Author of the conference)
CIRM (Publisher )
35K55 - Nonlinear parabolic equations
60H15 - Stochastic partial differential equations
60H30 - Applications of stochastic analysis (to PDE, etc.)
35Q84 - Fokker-Planck equations
CIRM (Publisher )
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Abstract :
In this work, we consider the discretization of some nonlinear Fokker-Planck-Kolmogorov equations. The scheme we propose preserves the non-negativity of the solution, conserves the mass and, as the discretization parameters tend to zero, has limit measure-valued trajectories which are shown to solve the equation. This convergence result is proved by assuming only that the coefficients are continuous and satisfy a suitable linear growth property with respect to the space variable. In particular, under these assumptions, we obtain a new proof of existence of solutions for such equations.
We apply our results to several examples, including Mean Field Games systems and variations of the Hughes model for pedestrian dynamics.
MSC Codes : We apply our results to several examples, including Mean Field Games systems and variations of the Hughes model for pedestrian dynamics.
35K55 - Nonlinear parabolic equations
60H15 - Stochastic partial differential equations
60H30 - Applications of stochastic analysis (to PDE, etc.)
35Q84 - Fokker-Planck equations
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 10/08/17 Conference Date : 10/08/17 Subseries : Research talks arXiv category : Analysis of PDEs Mathematical Area(s) : Probability & Statistics ; PDE Format : MP4 (.mp4) - HD Video Time : 00:56:02 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-08-10_Alvarez.mp4 
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Information on the Event
Event Title : CEMRACS: Numerical methods for stochastic models: control, uncertainty quantification, mean-field / CEMRACS : Méthodes numériques pour équations stochastiques : contrôle, incertitude, champ moyenEvent Organizers : Bouchard, Bruno ; Chassagneux, Jean-François ; Delarue, François ; Gobet, Emmanuel ; Lelong, Jérôme Dates : 17/07/17 - 25/08/17 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1556.html
Citation Data
DOI : 10.24350/CIRM.V.19205103Cite this video as: Silva Álvarez, Francisco José (2017). On the discretization of some nonlinear Fokker-Planck-Kolmogorov equations and applications. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19205103 URI : http://dx.doi.org/10.24350/CIRM.V.19205103 |
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