  We study an inverse boundary value problem on the determination of principal
order coefficients in isotropic nonautonomous heat flows stated as follows;
given a medium, and in the absence of heat sources and sinks, can the
time-dependent thermal conductivity and volumetric heat capacity of the medium
be uniquely determined from the Cauchy data of temperature and heat flux
measurements on its boundary? We prove uniqueness in all dimensions under an
assumption on the thermal diffusivity of the medium, which is defined as the
ratio of the thermal conductivity and volumetric heat capacity. As a corollary
of our result for isotropic media, we also obtain a uniqueness result, up to a
natural gauge, in two-dimensional anisotropic media. Our assumption on the
thermal diffusivity is related to construction of certain families of
exponential solutions to the heat equation.

Analysis of PDEs;Differential Geometry