Existence of Classical Solutions to a Stationary Simplified Quantum Energy-Transport Model in 1-Dimensional Space

The existence of classical solutions to a stationary simplified quantum energy-transport model for semiconductor devices in 1-dimensional space is proved. The model consists of a nonlinear elliptic third-order equation for the electron density, including a temperature derivative, an elliptic nonlinear heat equation for the electron temperature, and the Poisson equation for the electric potential. The proof is based on an exponential variable transformation and the Leray-Schauder fixed-point theorem.