Mathematical Sciences: Analytical and Numerical Approaches to Singular Perturbation Problems of Significance in Applications

本研究将研究的渐近解 非线性系统初边值问题 微分方程。 的解的一个特征 这些方程表现出在薄 地区 因此，渐近方法能够使 使用多个尺度的存在。 特别感兴趣的 本研究涉及边界和内部问题， 层次。 这项工作将受到物理应用的激励 包括模拟半导体操作的模型 装置. 问题将使用组合的分析 和数值方法。

This research will study the asymptotic solution of nonlinear initial and boundary value problems involving systems of differential equations. A characteristic of the solutions of these equations is that they exhibit rapid changes within thin regions. Consequently, the asymptotic methods are able to make use of the presence of multiple scales. Of particular interest in this research are problems involving boundary and interior layers. The work will be motivated by physical applications including models which simulate the operation of semiconductor devices. Problems will be attacked using a combined analytical and numerical approach.