Quantum Euler-Poisson Systems : existence of Stationary States
Quantum Euler-Poisson Systems : existence of Stationary States
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发表时间：
2002
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通讯作者：
A. Jüngel;Hai-liang Li
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作者：
A. Jüngel;Hai-liang Li
考虑了半导体中电子密度和静电势在有界区间内的一维量子Euler-Poisson系统。正电子密度强解的存在性和唯一性显示相当一般（可能非凸或非单调）的压力密度函数下的“亚音速”条件下，即假设足够小的电流密度。的证明是基于一个非线性椭圆四阶方程的电子密度的色散三阶方程，使用指数变换的变量的重新制定。
A one-dimensional quantum Euler-Poisson system for semiconductors for the electron density and the electrostatic potential in bounded intervals is considered. The existence and uniqueness of strong solutions with positive electron density is shown for quite general (possibly non-convex or non-monotone) pressure-density functions under a “subsonic” condition, i.e. assuming sufficiently small current densities. The proof is based on a reformulation of the dispersive third-order equation for the electron density as a nonlinear elliptic fourth-order equation using an exponential transformation of variables.