Existence and classical limit of stationary solutions to a one dimensional bipolar quantum drift diffusion equation

Journal of Shanghai Normal University (Natural Sciences)

LI Yeping¹  YANG Ting¹ 

[1] College of Mathematics and Sciences,Shanghai Normal University;

关键词: existence;    uniqueness;    classical limit;   

DOI  :  

来源: DOAJ

【 摘 要 】

We study the stationary solutions of a one-dimensional bipolar quantum drift-diffusion model from semiconductor devices and plasmas. In a bounded interval supplemented by the proper boundary conditions,we first show the existence and uniqueness of the stationary solutions to the one-dimensional bipolar quantum drift-diffusion model. The proof can be completed by the Schauder fixed-point principle and the careful energy estimates. Then,we study the classical limit of the stationary solutions to the bipolar quantum drift-diffusion model. Namely,we show that the stationary solution to the quantum drift-diffusion model approachesthat to the drift-diffusion model as the scaled Planck constant ε tends to zero.

【 授权许可】

Unknown