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

主要研究者将使用粘度溶液 技术来分析演化相变，奇异 随机控制和边界控制问题。 的工作 平均曲率流将导致更好地理解 微分几何与数学的关系 流体理论 平均曲率运动是 由其形状决定的表面。 演化界面 问题描述相变边界和运动， 物理材料。

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.