Existence analysis for a simplified transient energy‐transport model for semiconductors

A simplified transient energy‐transport system for semiconductors subject to mixed Dirichlet–Neumann boundary conditions is analyzed. The model is formally derived from the non‐isothermal hydrodynamic equations in a particular vanishing momentum relaxation limit. It consists of a drift‐diffusion‐type equation for the electron density, involving temperature gradients, a nonlinear heat equation for the electron temperature, and the Poisson equation for the electric potential. The global‐in‐time existence of bounded weak solutions is proved. The proof is based on the Stampacchia truncation method and a careful use of the temperature equation. Under some regularity assumptions on the gradients of the variables, the uniqueness of solutions is shown. Finally, numerical simulations for a ballistic diode in one space dimension illustrate the behavior of the solutions. Copyright © 2012 John Wiley & Sons, Ltd.