【作者】 刘芳；

【导师】 黎野平；

【作者基本信息】 华东理工大学 ， 应用数学， 2020， 硕士

【摘要】 本学位论文,考虑了一维双极量子漂移-扩散方程和三维双极量子漂移-扩散方程解的渐近行为。这种双极量子漂移-扩散方程是由椭圆抛物方程耦合而成,它可以用来描述半导体器件或者等离子体里的带电粒子的运动。我们首先考虑了在半空间上一维双极量子漂移-扩散方程解的渐近行为,它的渐近行为表现为相应的扩散波。其次,我们考虑了三维双极量子漂移-扩散方程初值问题解的大时间行为。即是,我们证明了三维双极量子漂移-扩散方程解的整体存在性,以及当时间t足够大时,其解以代数衰减率趋向平面扩散波。这些结论的证明由能量估计的办法得到。更多还原

【Abstract】 This dissertation considers the asymptotic behavior of solutions to the one-dimensional bipolar quantum drift-diffusion equation and the three-dimensional bipolar quantum drift-diffusion equation.This bipolar quantum drift-diffusion equation is coupled by an elliptic parabolic equation,and it can be used to describe the motion of charged particles in a semiconductor device or plasma.We first consider the asymptotic behavior of the solution of the one-dimensional bipolar quantum drift-diffusion equation on the half-space.Its asymptotic behavior is represented by the corresponding diffusion wave.Secondly,we consider the large-time behavior of the solution to the initial value problem of the three-dimensional bipolar quantum drift-diffusion equation.That is,we prove the overall existence of the solution of the three-dimensional bipolar quantum drift-diffusion equation,and when the time t is sufficiently large,its solution tends to a planar diffusion wave with an algebraic decay rate.Proof of these conclusions is obtained by the method of energy estimation.更多还原