Geodesic
Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition
Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 2, pp. 287-338

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We establish the convergence to the equilibrium for various linear collisional kinetic equations (including linearized Boltzmann and Landau equations) with physical local conservation laws in bounded domains with general Maxwell boundary condition. Our proof consists in establishing an hypocoercivity result for the associated operator; in other words, we exhibit a convenient Hilbert norm for which the associated operator is coercive in the orthogonal of the global conservation laws. Our approach allows us to treat general domains with all types of boundary conditions in a unified framework. In particular, our result includes the case of vanishing accommodation coefficient and thus the specific case of the specular reflection boundary condition.

Accepté le :
Publié le :
DOI : 10.4171/aihpc/44
Classification : 35-XX
Keywords: Kinetic equations 
@article{AIHPC_2023__40_2_287_0,
     author = {Bernou, Armand and Carrapatoso, Kleber and Mischler, St\'ephane and Tristani, Isabelle},
     title = {Hypocoercivity for kinetic linear equations in bounded domains with general {Maxwell} boundary condition},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {287--338},
     volume = {40},
     number = {2},
     year = {2023},
     doi = {10.4171/aihpc/44},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpc/44/}
}
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Bernou, Armand; Carrapatoso, Kleber; Mischler, Stéphane; Tristani, Isabelle. Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition. Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 2, pp. 287-338. doi: 10.4171/aihpc/44

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