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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Rates of convergence in slab geometry October 2017.pdf (382.18 Ko)
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