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Pré-Publication, Document De Travail Année : 2017

Rates of convergence to equilibrium for collisionless kinetic equations in slab geometry

Résumé

This work deals with free transport equations with partly di¤use sto-chastic boundary operators in slab geometry. Such equations are governed by stochastic semigroups in L 1 spaces: We prove convergence to equilibrium at the rate O t k 2(k+1)+1 (t ! +1) for L 1 initial data g in a suitable subspace of the domain of the generator T where k 2 N depends on the properties of the boundary operators near the tangential velocities to the slab. This result is derived from a quanti…ed version of Ingham's tauberian theorem by showing that Fg(s) := lim"!0 + (is + " T) 1 g exists as a C k function on Rn f0g such that d j ds j Fg(s) C jsj 2(j+1) near s = 0 and bounded as jsj ! 1 (0 j k) : Various preliminary results of independent interest are given and some related open problems are pointed out.
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Dates et versions

hal-01616055 , version 1 (13-10-2017)

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  • HAL Id : hal-01616055 , version 1

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Mustapha Mokhtar-Kharroubi, David Seifert. Rates of convergence to equilibrium for collisionless kinetic equations in slab geometry. 2017. ⟨hal-01616055⟩
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