The Mixed Boundary Value Problem Of The Quantum Hydrodynamic Model For Semiconductors In Thermal Equilibrium

In this paper, the two class mixed boundary value problems of the quantum hydrody-namic model for semiconductors in thermal equilibrium are investigated. 1. Unipolar case :where w₀,V₀ ∈ H¹(Ω) ∩ L^∞(Ω), w₀ ≥ 0 in Ω(?) R^d, 1≤ d < +∞, v is the outer unit normal on Γ_N. We show the existence and uniqueness of the solution and perform the semi-classical limit of the above system. 2. Bipolar case :where u₀, w₀, V₀ ∈ H¹(Ω) ∩ L^∞(Ω), u₀, w₀ ≥ 0 in Ω (?) R^d, 1 ≤ d ≤ 2, v is the outer unit normal on Γ_N. We show the existence and uniqueness of the solution of the above system.