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

本文研究非线性方程组的渐近解， 方程组的初边值问题 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。 这项工作的动机是物理应用，包括 模拟半导体器件操作的模型， 由最优控制引起的问题。 问题会被攻击 使用分析和数值相结合的方法。

This research will study the asymptotic solution of nonline- ar 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 is motivated by physical applications including models which simulate the operation of semiconductor devices and problems arising from optimal control. Problems will be attacked using a combined analytical and numerical approach.