“…This is exactly where the inverse problems theory comes in. More precisely, inverse problems theory consists of identifying some input parameters in a given system from a partial measurement on the solution, e.g., forcing terms [13,14,17], thermal conductivity and radiative coefficient [15], potential, damping coefficient and source terms [5,6,8], or initial temperature [21]. Up to our knowledge, the most practical and realistic measurements considered in literature use the state at a fixed final time.…”