论文标题
在降级费米恩气体的量子扩散描述中产生的非线性抛物线问题
On a nonlinear parabolic problem arising in the quantum diffusive description of a degenerate fermion gas
论文作者
论文摘要
本文从理论和数字上研究了一种非线性漂移扩散方程，描述了零温度极限中的费米子的气体。将方程式考虑在一个有界域的边界分为“绝缘”部分，施加了均匀的诺伊曼条件的“绝缘”部分，并在其中分配了非均匀的dirichlet数据，其中一个“接触”部分。通过假设简单的域配置证明了适合一类Dirichlet数据的固定解决方案的存在。通过数值实验研究了时间依赖性解决方案的长期行为，对于更复杂的域构型。
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.
