标题： 稳态漂移-扩散系统在狭窄凸域中的线性降维与同伦控制 显示英文标题

标题： Linear Reduction and Homotopy Control for Steady Drift-Diffusion Systems in Narrow Convex Domains

摘要： 本文开发并应用了先前工作中引入的结果，用于存在终止于期望解的同伦曲线的证明。 我们在第二部分描述了主要假设和结果；右逆近似是该理论的核心。 我们在第三部分将这一理论应用于基本的漂移-扩散方程。 载流子密度不假设满足玻尔兹曼统计，爱因斯坦关系也不假设成立。 通过证明同伦曲线的存在性，我们验证了预测/校正方案的基础计算框架，其中校正器使用了近似牛顿方法。 分析依赖于窄宽度域的假设。 然而，对域直径没有做出任何假设。 显示英文摘要

摘要： This article develops and applies results, originally introduced in earlier work, for the existence of homotopy curves, terminating at a desired solution. We describe the principal hypotheses and results in section two; right inverse approximation is at the core of the theory. We apply this theory in section three to the basic drift-diffusion equations. The carrier densities are not assumed to satisfy Boltzmann statistics and the Einstein relations are not assumed. By proving the existence of the homotopy curve, we validate the underlying computational framework of a predictor/corrector scheme, where the corrector utilizes an approximate Newton method. The analysis depends on the assumption of domains of narrow width. However, no assumption is made regarding the domain diameter.