Stationary solutions for a multi-dimensional nonisentropic hydrodynamic model for semiconductors

In this paper, we discuss a multi-dimensional stationary flow model for semiconductor devices which is based on the nonisentropic hydrodynamic equations with non-constant lattice temperature. We establish the existence of the irrotational non-thermal equilibrium subsonic steady state solutions with positive particle density and positive carrier temperature. The proofs are based on the Schauder fixed-point principle, Stampacchia’s truncation methods and the careful energy estimates. Meanwhile, we also show that these strong stationary solutions are unique.