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

Barletti, Luigi; Salvarani, Francesco (2016), On a Nonlinear Parabolic Problem arising in the Quantum Diffusive Description of a Degenerate Fermion Gas, SIAM Journal on Applied Mathematics, 76, 3, p. 867 - 886. 10.1137/140998263

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Type
Article accepté pour publication ou publié
Date
2016
Journal name
SIAM Journal on Applied Mathematics
Volume
76
Number
3
Publisher
Society for Industrial and Applied Mathematics
Pages
867 - 886
Publication identifier
Metadata
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Author(s)
Barletti, Luigi
Dipartimento di Matematica e Informatica [Firenze] [DiMal]
Salvarani, Francesco
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Dipartimento di matematica F. Casorati
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.
Subjects / Keywords
quantum drift diffusion; fermions; nonlinear parabolic equations; mixed boundary conditions