We present the quantitative method of the recent work [6] in a simple setting, together with a compactness argument that was not included in [6] and has interest per se. We are concerned with the exponential stabilisation (spectral gap) for linear kinetic equations with degenerate thermalisation, i.e. when the collision operator vanishes on parts of the spatial domain. The method in [6] covers both scattering and Fokker-Planck type operators, and deals with external potential and boundary conditions, but in these notes we present only its core argument and restrict ourselves to the kinetic Fokker-Planck in the periodic torus with unit velocities and a thermalisation degeneracy (this equation is not covered by the previous results [2, 9, 7]).
@article{SLSEDP_2021-2022____A11_0,
author = {Dietert, Helge and H\'erau, Fr\'ed\'eric and Hutridurga, Harsha and Mouhot, Cl\'ement},
title = {Trajectorial hypocoercivity and application to control theory},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:8},
pages = {1--10},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2021-2022},
doi = {10.5802/slsedp.156},
language = {en},
url = {http://www.numdam.org/articles/10.5802/slsedp.156/}
}
TY - JOUR AU - Dietert, Helge AU - Hérau, Frédéric AU - Hutridurga, Harsha AU - Mouhot, Clément TI - Trajectorial hypocoercivity and application to control theory JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:8 PY - 2021-2022 SP - 1 EP - 10 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/articles/10.5802/slsedp.156/ DO - 10.5802/slsedp.156 LA - en ID - SLSEDP_2021-2022____A11_0 ER -
%0 Journal Article %A Dietert, Helge %A Hérau, Frédéric %A Hutridurga, Harsha %A Mouhot, Clément %T Trajectorial hypocoercivity and application to control theory %J Séminaire Laurent Schwartz — EDP et applications %Z talk:8 %D 2021-2022 %P 1-10 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/articles/10.5802/slsedp.156/ %R 10.5802/slsedp.156 %G en %F SLSEDP_2021-2022____A11_0
Dietert, Helge; Hérau, Frédéric; Hutridurga, Harsha; Mouhot, Clément. Trajectorial hypocoercivity and application to control theory. Séminaire Laurent Schwartz — EDP et applications (2021-2022), Exposé no. 8, 10 p. doi : 10.5802/slsedp.156. http://www.numdam.org/articles/10.5802/slsedp.156/
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