Semiconductor devices are ubiquitous in the modern computer and telecommunications
industry. A precise knowledge of the transport equations for electron flow in semiconductors …

The relaxation time limit from the quantum Navier–Stokes–Poisson system to the quantum
drift–diffusion equation is performed in the framework of finite energy weak solutions. No …

Viscous stabilizations of the quantum hydrodynamic equations are studied. The quantum
hydrodynamic model consists of the conservation laws for the particle density, momen-tum …

We investigate the viscous model of quantum hydrodynamics in one and higher space
dimensions. Exploiting the entropy dissipation method, we prove the exponential decay to …

The existence of global-in-time weak solutions to the one-dimensional viscous quantum
hydrodynamic equations is proved. The model consists of the conservation laws for the …

The viscous quantum hydrodynamic equations for semiconductors with constant
temperature are numerically studied. The model consists of the one-dimensional Euler …

We shall investigate the asymptotic behavior of solutions to the Cauchy problem for the three-
dimensional quantum Navier–Stokes–Poisson system. We first establish the stationary …

In this article, fifth order finite volume multi-resolution weighted essentially non-oscillatory
(MR-WENO) scheme is developed for solving one-dimensional non linear viscous quantum …

A viscous quantum hydrodynamic system for particle density, current density, energy
density, and electrostatic potential, coupled with a Poisson equation, is studied in spatial …

We formally derive two nonlinear Ginzburg-Landau type models starting from the Wigner-
Fokker-Planck system, which rules the evolution of a quantum electron gas interacting with a …