On a nonlinear parabolic problem arising in the quantum diffusive description of a degenerate fermion gas
Analysis of PDEs
2020-06-05 v1 Mathematical Physics
math.MP
Abstract
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 nonhomogeneous 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.
Keywords
Cite
@article{arxiv.2006.02992,
title = {On a nonlinear parabolic problem arising in the quantum diffusive description of a degenerate fermion gas},
author = {Luigi Barletti and Francesco Salvarani},
journal= {arXiv preprint arXiv:2006.02992},
year = {2020}
}