Jean Morlet Chair 2021- Conference: Kinetic Equations: From Modeling Computation to Analysis / Chaire Jean-Morlet 2021 - Conférence : Equations cinétiques : Modélisation, Simulation et Analyse

Collection Jean Morlet Chair 2021- Conference: Kinetic Equations: From Modeling Computation to Analysis / Chaire Jean-Morlet 2021 - Conférence : Equations cinétiques : Modélisation, Simulation et Analyse

Organizer(s) Bostan, Mihaï ; Jin, Shi ; Mehrenberger, Michel ; Montibeller, Celine

Date(s) 22/03/2021 - 26/03/2021

linked URL https://www.chairejeanmorlet.com/2355.html

00:00:00 / 00:00:00

8 19

Large time asymptotics for evolution equations with mean field couplings

By Jean Dolbeault

This lecture is devoted to the characterization of convergence rates in some simple equations with mean field nonlinear couplings, like the Keller-Segel and Nernst-Planck systems, Cucker-Smale type models, and the Vlasov-Poisson-Fokker-Planck equation. The key point is the use of Lyapunov functionals adapted to the nonlinear version of the model to produce a functional framework adapted to the asymptotic regime and the corresponding spectral analysis.

Information about the video

Date of recording 25/03/2021
Date of publication 09/04/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19733603
Cite this video Dolbeault, Jean (25/03/2021). Large time asymptotics for evolution equations with mean field couplings. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19733603
URL https://dx.doi.org/10.24350/CIRM.V.19733603

Domain(s)

Analysis of PDEs

Bibliography

ADDALA, Lanoir, DOLBEAULT, Jean, LI, Xingyu, et al. L2-Hypocoercivity and large time asymptotics of the linearized Vlasov-Poisson-Fokker-Planck system. arXiv preprint arXiv:1909.12762, 2019. - https://arxiv.org/abs/1909.12762
ARNOLD, Anton, DOLBEAULT, Jean, SCHMEISER, Christian, et al. Sharpening of decay rates in Fourier based hypocoercivity methods. arXiv preprint arXiv:2012.09103, 2020. - https://arxiv.org/abs/2012.09103
DOLBEAULT, Jean et LI, Xingyu. φ-entropies: Convexity, coercivity and hypocoercivity for Fokker–Planck and kinetic Fokker–Planck equations. Mathematical Models and Methods in Applied Sciences, 2018, vol. 28, no 13, p. 2637-2666. - https://arxiv.org/abs/1712.09897
LI, Xingyu. Asymptotic behavior of Nernst-Planck equation. arXiv preprint arXiv:1910.04477, 2019. - https://arxiv.org/abs/1910.04477
LI, Xingyu. Flocking: Phase transition and asymptotic behaviour. arXiv preprint arXiv:1906.07517, 2019. - https://arxiv.org/abs/1906.07517

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Jean_DOLBEAULT.pdf

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