Mathematical Sciences: Nonlinear Differential Equations in Solidification Theory

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This research will continue an investigation of the phase field approach to solidification. This approach has resulted in a uniform way of understanding phase boundaries. The difference between a thin and sharp interface will be considered, especially the effect of the difference on instability. Anisotropy will be studied using various analytical and numerical methods. Also considered will be the interface between a solid and liquid when the interface is in contact with an external boundary. The related problem for alloys will be investigated.