Determination of small linear perturbations in the diffusion coefficient from partial dynamic boundary measurements

This work deals with an inverse boundary value problem arising from the equation of heat conduction. We reconstruct small perturbations of the (isotropic) heat conductivity distribution from partial (on accessible part of the boundary) dynamic boundary measurements and for finite interval in time. By constructing of appropriate test functions, using a control method, we provide a rigorous derivation of the inverse Fourier transform of the perturbations in the diffusion coefficient as the leading order of an appropriate averaging of the partial dynamic boundary measurements.