Mathematical Sciences: Analytical and Algorithmic Studies for Nonlinear Systems of Multiple Subtypes

这项研究将从分析和算法的角度研究与半导体器件系统相关的非线性偏微分方程组。这些方程是椭圆型/双曲型或椭圆型/抛物型/双曲型。这项研究的一部分将继续研究漂移-扩散模型，并审查与快速变化的系数有关的问题。第二部分将使用TVD方案来检查水动力模型。这项工作中考虑的模型应该会增加对当前感兴趣的多谷半导体的理解，例如砷化镓。

This research will study nonlinear partial differential equations associated with the semiconductor device system from both an analytical and algorithmic point of view. These equations are of elliptic/hyperbolic or elliptic/parabolic/ hyperbolic subtypes. One part of this research will continue work on a drift-diffusion model and examine issues related to rapidly changing coefficients. A second portion will use the TVD scheme to examine a hydrodynamic model. The models considered in this work should increase understanding of multi-valley semiconductors currently of interest, such as gallium arsenide.