Franklin

Factorization of non-symmetric operators and exponential H-theorem / M.P. Gualdani, S. Mischler, C. Mouhot.

Author/Creator:
Gualdani, Maria Pia, 1976- author.
Publication:
Paris : Société Mathématique de France, 2017.
Format/Description:
Book
137 pages : illustration ; 24 cm.
Series:
Mémoire (Société mathématique de France) ; 0249-633X nouv. sér., no 153.
Mémoires de la Société Mathématique de France. Nouvelle série, 0249-633X ; numéro 153, nouvelle série
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Subjects:
Banach spaces.
Semigroups.
Spectral theory (Mathematics).
Fokker-Planck equation.
Language:
Abstracts in English and French.
Summary:
"We present an abstract method for deriving decay estimates on the resolvents and semigroups of non-symmetric operators in Banach spaces, in terms of estimates in another smaller reference Banach space. The core of the method is a high-order quantitative factorization argument on the resolvents and semigroups, and it makes use of a semigroup commutator condition of regularization. We then apply this approach to the Fokker-Planck equation, to the kinetic Fokker-Planck equation in the torus, and to the linearized Boltzmann equation in the torus. Thanks to the latter results and to a non-symmetric energy method, we obtain the first constructive proof of exponential decay, with sharp rate, towards global equilibrium for the full non-linear Boltzmann equation for hard spheres, conditionally to some smoothness and (polynomial) moment estimates; this solves a conjecture about the optimal decay rate of the relative entropy in the H-theorem"--Back cover.
Notes:
Includes bibliographical references (pages [127]-137).
Contributor:
Mischler, Stéphane, author.
Mouhot, Clément, author.
ISBN:
9782856298749
2856298745
OCLC:
1031372143
Publisher Number:
9782856298749
99980507724