Mathematical Sciences: Some Non-Classical Problems in Partial Differential Equations with Trace Type Functional Coefficients

数学科学：带有痕型函数系数的偏微分方程中的一些非经典问题

• 批准号: 8901301
• 负责人: John Cannon
• 金额: $ 6.16万
• 依托单位: Lamar University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901301&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Non; Classical

8901301 Cannon Free boundary and inverse problems arise in the modelling of many physically important phenomena. One example of the former is to determine the location of the water/ice interface in a region where the temperature on the boundary of the region is specified so as to be subcritical in some locations and supercritical in others. Inverse problems arise, for instance, in the attempt to locate the heat source inside an object by measuring the temperature and heat flux at the surface. Free boundary and inverse problems of this type are included in the study of a certain class of partial differential equations whose coefficients may depend on functionals of the solution. This project examines questions of existence and unicity of solutions and seeks to provide a better understanding of this class of differential equations.

8901301 Cannon 在许多重要物理现象的建模中会出现自由边界和反演问题。 前者的一个示例是确定某一区域中水/冰界面的位置，其中该区域边界上的温度被指定为在一些位置为亚临界而在其他位置为超临界。 例如，当试图通过测量表面的温度和热通量来定位物体内部的热源时，就会出现逆问题。 这种类型的自由边界和反问题包含在某一类偏微分方程的研究中，其系数可能取决于解的泛函。 该项目研究解的存在性和唯一性问题，并寻求更好地理解此类微分方程。