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We consider the inverse source problem of determining a source term dependingon both time and space variable for fractional and classical diffusionequations in a cylindrical domain from boundary measurements. With suitableboundary conditions we prove that some class of source terms which areindependent of one space direction, can be reconstructed from boundarymeasurements. Actually, we prove that this inverse problem is well-posed. Weestablish also some results of Lipschitz stability for the recovery of sourceterms which we apply to the stable recostruction of time-dependentcoefficients.

Reconstruction and stable recovery of source terms and coefficients appearing in diffusion equations