Existence of weak solutions to a stationary 1-dimensional bipolar quantum energy-transport model - Dong, Jianwei; Cheng, Chunrui; Wang, Yanping (Zhejiang da xue xue bao. Journal of Zhejiang University. Sciences edition. Li xue ban, 2016)
A stationary bipolar quantum energy-transport model for semiconductors is studied in a 1-dimensional bounded domain. The model is reformulated as a coupled system consisting of two fourth-order elliptic equations and a second-order degenerate elliptic equation. The existence of weak solutions to the reformulated system is proved using the truncation method and the Leray-Schauder fixed-point theorem.