Underground geotechnical or civil engineering works change the primary stressed and strained state of the rock mass and subsequently the fields of displacement and stresses. A significant effect of these changes is the formation of subsidence in the earth’s surface with significant negative economic or other consequences. In a series of recent works, large-scale subsidence in geostructures was modelled using Litwiniszyn’s theory (Einstein–Kolmogorov Differential Equation) and the trap-door mechanism. The solution of the Inverse Subsidence Diffusion–Convection (ISDC) problem – which belongs to the class of backward parabolic problems – provides the base (gravity-directed) displacement using the surface subsidence as ‘initial’ condition. Early well-posedness of the initial and boundary value problems has already been examined (in terms of stability estimates) in previous papers. In this work, study of control estimates and well-posedness of the ISDC problem, using energy method, are discussed.