Katie Gittins

Inverse problems and continuity of heat content coefficients

We consider the Open heat content of convex, planar domains. That is, the amount of heat left inside the domain at a later time if the initial temperature of the domain is one, the initial temperature of the exterior is zero, and no temperature conditions are imposed on the boundary.
We investigate whether the small-time asymptotic expansion of the Open heat content can determine certain polygons, and we study the continuity of the geometric coefficients in this expansion along sequences of convex sets.
This is based on joint work with Ryoki Endo and Jacob Walker.