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

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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.