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

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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.