Subsonic solutions of hydrodynamic model for semiconductors

Abstract

This paper is concerned with the existence and uniqueness of the steady‐state solution of hydrodynamic model for semiconductor devices. Boundary conditions are prescribed by vorticity on inflow boundary as well as by electron density, temperature, and normal component of electron velocity on whole boundary. If the ambient temperature is large, and if both vorticity on inflow boundary and the variation of density on boundary are small, a unique subsonic solution exists. © 1997 by B.G. Teubner Stuttgart–John Wiley & Sons Ltd.

3-D axisymmetric subsonic flows with nonzero swirl for the compressible Euler–Poisson system

“…The goal of this work is to prove the structural stability of three dimensional axially symmetric subsonic flows with nonzero swirl(=nonzero angular momentum) to the system (1.5) for non small boundary data. The existence and the uniqueness of subsonic flows to Euler-Poisson system were proved in [1,3,4,5,6,10,11,26,29,31]. In [10,11], the unique existence of subsonic flows for Euler-Poisson system is proved for small data.…”

“…In [10,11], the unique existence of subsonic flows for Euler-Poisson system is proved for small data. Subsonic flows with small current flux were studied in [1,3,26,31]. The structural stability of subsonic flows for multidimensional potential flow and two dimensional flow with nonzero vorticity was proved in [4,5,6], where no smallness of data was assumed.…”

“…The existence and the uniqueness of subsonic flows to Euler-Poisson system were proved in [1,3,4,5,6,10,11,26,29,31]. In [10,11], the unique existence of subsonic flows for Euler-Poisson system is proved for small data.…”

Existence of the Rotational Subsonic Stationary Solution for a Two-Dimensional Bipolar Euler-Poisson Equation

“…Gamba and Morawetz [11] studied a viscous approximation of transonic solution in the two dimensional semiconductor equations. Degond and Markowich [12] and Yeh [13] established the irrotational subsonic stationary solutions for a multi-dimensional unipolar isentropic Euler-Poisson equations, respectively. Markowich [14] showed the existence of rotational subsonic solutions for the two-dimensional steady-state Euler-Poisson equations.…”

On Steady Subsonic Flows for Euler--Poisson Models

“…Also, the author used a smallness assumption on the physical parameter multiplying the drift-term in the velocity equations instead in the irrotational 3-D case and obtained similar results. For the full hydrodynamic model,Yeh [20] showed the existence of a unique strong solution in several space dimensions if the flow is subsonic, the ambient temperature is large enough, and the vorticity on the inflow boundary and the variation of the electron density on the boundary are sufficiently small. Zhu and Hattori [21] proved the existence of classical subsonic solutions in one space dimension for the whole space problem under the additional assumption that the doping profile be close to a constant.…”