Analytical and Geometrical Problems in Non Linear Partial Differential Equations

非线性偏微分方程中的解析和几何问题

• 批准号: 0654267
• 负责人: Luis Caffarelli
• 金额: $ 60.03万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-06-01 至 2013-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0654267&HistoricalAwards=false
• 关键词: Analytical; Geometrical; Problems; Non; Linear

Analytical and Geometrical Problems in Nonlinear Partial Differential EquationsAbstract of Proposed Research Luis CaffarelliThis research is to study the mathematical analysis of a number of scientific phenomena that are modeled by nonlinear partial differential equations. Specific topics include the properties of solutions of nonlinear problems involving anomalous (in particular integral) diffusion processes, such as phase transitions, fluid dynamics and optimal control. Also nonlinear random homogenization of fully non linear equations or constrained problems in randomly perforated domains. Antenna design for general signal propagation laws, and other Minkowski type problemsSpecific examples of the type of phenomena being studied include the analysis of equations modeling boundary control (optimizing insulation shape across a surface, or the behavior of semi permeable membranes), surface flame propagation and the pricing of options when processes are highly discontinuous ( Levi processes). Also the effective heating of a family of small, randomly distributed, heating sources, the propagation of a flame on a medium with random occlusions or the sliding of a drop on a rough surface and the design of an optimal reflecting surface in a periodic medium.

非线性偏微分方程中的分析和几何问题--研究建议摘要 路易斯·卡法雷利本研究旨在研究一些由非线性偏微分方程建模的科学现象的数学分析。 具体的主题包括涉及异常（特别是积分）扩散过程，如相变，流体动力学和最优控制的非线性问题的解决方案的属性。 也可用于完全非线性方程组的非线性随机均匀化或随机开孔区域中的约束问题。天线设计一般的信号传播规律，和其他闵可夫斯基型problemsSpecific的例子类型的现象正在研究包括方程建模边界控制（优化绝缘形状在一个表面，或行为的半透膜），表面火焰传播和定价的过程是高度不连续的选项（列维过程）的分析。也是一个家庭的小，随机分布，热源，火焰的传播与随机闭塞的介质或一滴在粗糙表面上的滑动和周期性介质中的最佳反射表面的设计的有效加热。