English
Mean-field-type limits of interacting particle systems for multiple species
Virtualconference
Auteurs : Juengel, Ansgar (Auteur de la conférence)
CIRM (Editeur )
35K45 - Initial value problems for pararabolic systems
60J70 - Applications of diffusion theory (population genetics, absorption problems, etc.), See also {92Dxx}
82C22 - Interacting particle systems
35Q92 - PDEs in connection with biology and other natural sciences
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Ansgar_Jungel.pdf
CIRM (Editeur )
Loading the player...
|
Résumé :
The aim of this talk is the rigorous derivation of crossdiffusion systems from stochastic, moderately interacting many-particle systems for multiple species. Applications include animal populations and neuronal ensembles. The mean-field limit leads to nonlocal cross-diffusion systems, while the limit of vanishing interaction radius gives local cross-diffusion equations. This allows for the derivation of fluid-type models that can be found in neuronal networks and of Shigesada-Kawasaki-Teramoto population models. The derivation uses the techniques of Oehlschläger. The entropy structure of the limiting models is discussed and some numerical experiments are presented.
Codes MSC : 35K45 - Initial value problems for pararabolic systems
60J70 - Applications of diffusion theory (population genetics, absorption problems, etc.), See also {92Dxx}
82C22 - Interacting particle systems
35Q92 - PDEs in connection with biology and other natural sciences
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Ansgar_Jungel.pdf
|
Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 09/04/2021 Date de Captation : 22/03/2021 Sous Collection : Research talks Catégorie arXiv : Analysis of PDEs Domaine(s) : EDP ; Probabilités & Statistiques Format : MP4 (.mp4) - HD Durée : 00:27:41 Audience : Chercheurs Download : https://videos.cirm-math.fr/2021-03-22_Juengel.mp4 
|
Informations sur la Rencontre
Nom de la Rencontre : Jean Morlet Chair 2021- Conference: Kinetic Equations: From Modeling Computation to Analysis / Chaire Jean-Morlet 2021 - Conférence : Equations cinétiques : Modélisation, Simulation et AnalyseOrganisateurs de la Rencontre : Bostan, Mihaï ; Jin, Shi ; Mehrenberger, Michel ; Montibeller, Celine Dates : 22/03/2021 - 26/03/2021 Année de la rencontre : 2021 URL de la Rencontre : https://www.chairejeanmorlet.com/2355.html
Données de citation
DOI : 10.24350/CIRM.V.19734603Citer cette vidéo: Juengel, Ansgar (2021). Mean-field-type limits of interacting particle systems for multiple species. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19734603 URI : http://dx.doi.org/10.24350/CIRM.V.19734603 |
Voir Aussi
- [Virtualconference] Model predictive and random batch methods for a guiding problem / Auteur de la conférence Zuazua, Enrique.
- [Virtualconference] A De Giorgi argument for $L^{\infty}$ solution to the Boltzmann equation without angular cutoff / Auteur de la conférence Yang, Tong.
- [Virtualconference] An asymptotic preserving method for Levy Fokker Planck equation with fractional diffusion limit / Auteur de la conférence Wang, Li.
- [Virtualconference] Bacterial movement by run and tumble: models, patterns, pathways, scales / Auteur de la conférence Perthame, Benoît.
- [Virtualconference] Quantitative De Giorgi methods in kinetic theory / Auteur de la conférence Mouhot, Clément.
- [Virtualconference] Stable and unstable steady states for the HMF model / Auteur de la conférence Mehats, Florian.
- [Virtualconference] Highly-oscillatory evolution equations: averaging and numerics / Auteur de la conférence Lemou, Mohammed.
- [Virtualconference] An inverse problem for a model of cell motion and chemotaxis / Auteur de la conférence Klingenberg, Christian.
- [Virtualconference] Large stochastic systems of interacting particles / Auteur de la conférence Jabin, Pierre-Emmanuel.
- [Virtualconference] A new stability and convergence proof of the Fourier-Galerkin spectral method for the spatially homogeneous Boltzmann equation / Auteur de la conférence Hu, Jingwei.
- [Virtualconference] Stabilization of random kinetic equations / Auteur de la conférence Herty, Michael.
- [Virtualconference] Classical and quantum particles coupled to a vibrational environment / Auteur de la conférence Goudon, Thierry.
- [Virtualconference] Partial regularity in time for the Landau equation with Coulomb interaction / Auteur de la conférence Golse, François.
- [Virtualconference] Dynamical low-rank approximation for radiation transport / Auteur de la conférence Frank, Martin.
- [Virtualconference] Large time asymptotics for evolution equations with mean field couplings / Auteur de la conférence Dolbeault, Jean.
- [Virtualconference] Quasilinear approximation of Vlasov and Liouville equations / Auteur de la conférence Bardos, Claude.
- [Virtualconference] Collective dynamics of quantized vortices in superfluidity and superconductivity / Auteur de la conférence Bao, Weizhu.
- [Virtualconference] Modal based hypocoercivity methods on the torus and the real line with application to Goldstein-Taylor models / Auteur de la conférence Arnold, Anton.
Bibliographie
