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

数学科学：具有极大值原理的非线性偏微分方程及其在最优控制和相变中的应用

• 批准号: 9200801
• 负责人: Halil Soner
• 金额: $ 10.09万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9200801&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Partial; Differential

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.

首席研究员将使用粘度求解技术来分析演化相变、奇异随机控制和边界控制问题。 对平均曲率流的研究将有助于更好地理解微分几何与流体数学理论之间的关系。 平均曲率运动是由形状决定的表面演化的一个例子。 演化界面问题描述了物理材料中的相变边界和运动。