Mathematical Sciences: Nonlinear Partial Differential Equations with Maximum Principle and Their Applications to Optimal Control and Phase Transitions

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The principal investigator will use viscosity solution techniques to analyse evolutionary phase transitions, singular stochastic controls, and boundary control problems. The work on mean curvature flows will lead to a better understanding of the relation between differential geometry and the mathematical theory of fluids. Motion by mean curvature is one example of evolution of surfaces determined by their shape. Evolutionary interface problems describe phase transition boundaries and the motion in physical materials.