Details

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