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In this note, we investigate the spectral analysis and long time asymptotic convergence of semigroups associated to discrete, fractional and classical Fokker-Planck equations in some regime where the corresponding operators are close. We successively deal with the discrete and the classical Fokker-Planck model and the fractional and the classical Fokker-Planck model. In each case, we present results of uniform convergence to equilibrium based on perturbation and/or enlargement arguments and obtained in collaboration with S. Mischler in [7].
@article{SLSEDP_2015-2016____A10_0,
author = {Tristani, Isabelle},
title = {Convergence to equilibrium for linear {Fokker-Planck} equations},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:10},
pages = {1--14},
publisher = {Institut des hautes des scientifiques & Centre de mathtiques Laurent Schwartz, ole polytechnique},
year = {2015-2016},
doi = {10.5802/slsedp.83},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/slsedp.83/}
}
TY - JOUR AU - Tristani, Isabelle TI - Convergence to equilibrium for linear Fokker-Planck equations JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:10 PY - 2015-2016 SP - 1 EP - 14 PB - Institut des hautes des scientifiques & Centre de mathtiques Laurent Schwartz, ole polytechnique UR - http://geodesic.mathdoc.fr/articles/10.5802/slsedp.83/ DO - 10.5802/slsedp.83 LA - en ID - SLSEDP_2015-2016____A10_0 ER -
%0 Journal Article %A Tristani, Isabelle %T Convergence to equilibrium for linear Fokker-Planck equations %J Séminaire Laurent Schwartz — EDP et applications %Z talk:10 %D 2015-2016 %P 1-14 %I Institut des hautes des scientifiques & Centre de mathtiques Laurent Schwartz, ole polytechnique %U http://geodesic.mathdoc.fr/articles/10.5802/slsedp.83/ %R 10.5802/slsedp.83 %G en %F SLSEDP_2015-2016____A10_0
Tristani, Isabelle. Convergence to equilibrium for linear Fokker-Planck equations. Séminaire Laurent Schwartz — EDP et applications (2015-2016), Exposé no. 10, 14 p. doi : 10.5802/slsedp.83. http://geodesic.mathdoc.fr/articles/10.5802/slsedp.83/
[1] Gentil, I., and Imbert, C. The Lévy-Fokker-Planck equation: -entropies and convergence to equilibrium. Asymptot. Anal. 59, 3-4 (2008), 125–138.
[2] Gualdani, M. P., Mischler, S., and Mouhot, C. Factorization of non-symmetric operators and exponential -Theorem. (2013) . | HAL
[3] Mischler, S. Semigroups in Banach spaces, factorisation and spectral analysis. Work in progress.
[4] Mischler, S., and Mouhot, C. Exponential stability of slowly decaying solutions to the Kinetic-Fokker-Planck equation. (2014) , to appear in Arch. Rational Mech. Anal. | HAL
[5] Mischler, S., and Mouhot, C. Stability, convergence to self-similarity and elastic limit for the Boltzmann equation for inelastic hard spheres. Comm. Math. Phys. 288, 2 (2009), 431–502.
[6] Mischler, S., and Scher, J. Semigroup spectral analysis and growth-fragmentation equation. (2012) , to appear in Annales de l’Institut Henri Poincaré, Analyse Non Linéaire. | HAL
[7] Mischler, S., and Tristani, I. Uniform semigroup spectral analysis of the discrete, fractional & classical Fokker-Planck equations. (2015) . | HAL
[8] Mouhot, C. Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials. Comm. Math. Phys. 261, 3 (2006), 629–672.
[9] Tristani, I. Boltzmann equation for granular media with thermal force in a weakly inhomogeneous setting. (2013) , to appear in J. Funct. Anal. | HAL
[10] Tristani, I. Fractional Fokker-Planck equation. Commun. Math. Sci. 13, 5 (2015), 1243–1260.
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