1,104 research outputs found
On a drift-diffusion system for semiconductor devices
In this note we study a fractional Poisson-Nernst-Planck equation modeling a
semiconductor device. We prove several decay estimates for the Lebesgue and
Sobolev norms in one, two and three dimensions. We also provide the first term
of the asymptotic expansion as .Comment: to appear in Annales Henri Poincar\'
Uniform semigroup spectral analysis of the discrete, fractional \& classical Fokker-Planck equations
In this paper, we investigate the spectral analysis (from the point of view
of semi-groups) of discrete, fractional and classical Fokker-Planck equations.
Discrete and fractional Fokker-Planck equations converge in some sense to the
classical one. As a consequence, we first deal with discrete and classical
Fokker-Planck equations in a same framework, proving uniform spectral estimates
using a perturbation argument and an enlargement argument. Then, we do a
similar analysis for fractional and classical Fokker-Planck equations using an
argument of enlargement of the space in which the semigroup decays. We also
handle another class of discrete Fokker-Planck equations which converge to the
fractional Fokker-Planck one, we are also able to treat these equations in a
same framework from the spectral analysis viewpoint, still with a semigroup
approach and thanks to a perturbative argument combined with an enlargement
one. Let us emphasize here that we improve the perturbative argument introduced
in [7] and developed in [11], relaxing the hypothesis of the theorem, enlarging
thus the class of operators which fulfills the assumptions required to apply
it
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