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Article Dans Une Revue SIAM Journal on Applied Mathematics Année : 2016

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

Résumé

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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Dates et versions

hal-01432839 , version 1 (12-01-2017)

Licence

Paternité - Pas d'utilisation commerciale - Pas de modification

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Luigi Barletti, Francesco Salvarani. On a Nonlinear Parabolic Problem arising in the Quantum Diffusive Description of a Degenerate Fermion Gas. SIAM Journal on Applied Mathematics, 2016, 76, pp.867 - 886. ⟨10.1137/140998263⟩. ⟨hal-01432839⟩
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