Large time asymptotics for evolution equations with mean field couplings | Vidéo | Carmin.tv

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Large time asymptotics for evolution equations with mean field couplings

By Jean Dolbeault

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

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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