A Heat Source Reconstruction Formula from Single Internal Measurements Using a Family of Null Controls

We consider the inverse problem of determining the spatial dependence of the source term in a heat equation in assuming known, from a single internal measurements of the solution in . The purpose of this paper is to establish a reconstruction formula for similar to the one obtained by M. Yamamoto in "Stability, Reconstruction formula and regularization for an inverse source hyperbolic problem by a control method", Inverse Problems 11 (1995), 481-496, for hyperbolic equations using exact controls, and generalized here for parabolic equations. The reconstruction formula is associated to a family of exact controls indexed by . We perform numerical simulations in order to illustrate the feasibility, accuracy and stability of the proposed reconstruction formula. © 2013 by Walter de Gruyter Berlin Boston 2013.