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

8901301 大炮 在模拟中出现了自由边界和反问题 许多重要的物理现象。 的一个示例 前者是确定水/冰界面的位置 在一个区域中，该区域边界上的温度 规定在某些位置为亚临界， 超临界在其他 例如，出现了逆问题， 在试图定位物体内部的热源时， 测量表面的温度和热通量。 这类自由边界和反问题是 包括在对某类局部的研究中， 系数可能依赖于 解的泛函。 这个项目研究的问题 解决办法的存在性和唯一性，并寻求提供一个 更好地理解这类微分方程。

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.