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

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