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A. Jüngel, R. Pinnau, E. Röhrig:
"Existence analysis for a simplified transient energy-transport model for semiconductors";
Mathematical Methods in the Applied Sciences, 36 (2013), S. 1701 - 1712.

Siehe englisches Abstract.

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.

Energy-transport equations; semiconductors

http://dx.doi.org/10.1002/mma.2715