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

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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.