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On a Nonlinear Parabolic Problem arising in the Quantum Diffusive Description of a Degenerate Fermion Gas

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BaSa_SIAP-revised_2.pdf (818.6Kb)
Date
2016
Dewey
Analyse
Sujet
quantum drift diffusion; fermions; nonlinear parabolic equations; mixed boundary conditions
Journal issue
SIAM Journal on Applied Mathematics
Volume
76
Number
3
Publication date
05-2016
Article pages
867 - 886
Publisher
Society for Industrial and Applied Mathematics
DOI
http://dx.doi.org/10.1137/140998263
URI
https://basepub.dauphine.fr/handle/123456789/17271
Collections
  • CEREMADE : Publications
Metadata
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Author
Barletti, Luigi
228230 Dipartimento di Matematica e Informatica [Firenze] [DiMal]
Salvarani, Francesco
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
30138 Dipartimento di matematica F. Casorati
Type
Article accepté pour publication ou publié
Abstract (EN)
This article studies, both theoretically and numerically, a nonlinear drift-diffusion equation describing a gas of fermions in the zero-temperature limit. The equation is considered on a bounded domain whose boundary is divided into an insulating " part, where homogeneous Neumann conditions are imposed, and a " contact " part, where non-homogeneous Dirichlet data are assigned. The existence of stationary solutions for a suitable class of Dirichlet data is proven by assuming a simple domain configuration. The long-time behavior of the time-dependent solution, for more complex domain configurations, is investigated by means of numerical experiments.

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