The stationary solution of a one-dimensional bipolar quantum hydrodynamic model

2021 ◽  
Vol 493 (1) ◽  
pp. 124537
Author(s):  
Jing Hu ◽  
Yeping Li ◽  
Jie Liao
Keyword(s):  
Stationary Solution ◽  
Hydrodynamic Model ◽  
One Dimensional ◽  
Quantum Hydrodynamic Model ◽  
Quantum Hydrodynamic

The combined semi-classical and relaxation limit in a quantum hydrodynamic semiconductor model

2010 ◽  
Vol 140 (1) ◽  
pp. 119-134 ◽  
Author(s):  
Yeping Li
Keyword(s):  
Diffusion Model ◽  
Hydrodynamic Model ◽  
Drift Diffusion Model ◽  
Smooth Solutions ◽  
Drift Diffusion ◽  
One Dimensional ◽  
Quantum Hydrodynamic Model ◽  
Highly Nonlinear ◽  
Isentropic Euler Equations ◽  
Quantum Hydrodynamic

We discuss the combined semi-classical and relaxation limit of a one-dimensional isentropic quantum hydrodynamical model for semiconductors. The quantum hydrodynamic equations consist of the isentropic Euler equations for the particle density and current density, including the quantum potential and a momentum relaxation term. The momentum equation is highly nonlinear and contains a dispersive term with third-order derivatives. The equations are self-consistently coupled to the Poisson equation for the electrostatic potential. With the help of the Maxwell-type iteration, we prove that, as the relaxation time and Planck constant tend to zero, periodic initial-value problems of a scaled one-dimensional isentropic quantum hydrodynamic model have unique smooth solutions existing in the time interval where the classical drift-diffusion model has smooth solutions. Meanwhile, we justify a formal derivation of the classical drift-diffusion model from the quantum hydrodynamic model.

Sign in / Sign up

Export Citation Format

Share Document