On a steady state euler-poisson model for semiconduc

Abstract

The Euler-Poisson model, a simplified version of the hydrodynamic model for semiconductor devices, consists of a first order nonlinear system coupled to Poisson`s equation. The nonlinear system is just the steady state Euler equations of gas dynamics for a gas of charged particles in a electric field that includes a velocity relaxation term. In the one-dimensional steady state case, the differential equations are elliptic in the subsonic regions, and hyperbolic/elliptic in the transonic regions solution in the one-dimensional case, we refer researchers. For a transonic solution in the one-dimensional case are discussed. They prescribed boundary conditions for electron density and are discussed. They prescribed boundary conditions for electron density and electrostatic potential, and showed that if the current density is small enough, a unique subsonic solution exists. In it was shown that the existence of a subsonic solution in the two-dimensional case, though uniqueness of solution is unknown. Furthermore, in existence and uniqueness of a subsonic solution were proved for potential flow in the three-dimensional case. Without the potential flow assumption, we study in this paper the existence of a subsonic solution in the three-dimensional case. By prescribing a vorticity on inflow boundary, a small normal component of velocity onmore » the whole boundary, and assuming a small variation of the velocity relaxation time in the entire semiconductor domain, we prove the existence of a smooth subsonic solution by the Schauder fixed point theorem. Then, a way of prescribing admissible vorticities on the inflow boundary so that subsonic solutions exist is discussed.« less