F. Brezzi et al., THERMAL-EQUILIBRIUM STATES OF THE QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTORS IN ONE-DIMENSION, Applied mathematics letters, 8(1), 1995, pp. 47-52
The thermal equilibrium of the quantum hydrodynamic model for semicond
uctors is investigated in one space dimension. Existence is obtained u
sing a fixed point argument. Uniqueness is proved for small values of
the scaled Planck constant. The classical limit is also carried out.