Data compatibility and conditional stability for an inverse source problem in the heat equation

An inverse problem of determining a nonlinear source term in a heat equation via final observations is investigated. By applying integral identity method, data compatibilities are obtained with which the inverse source problem here is proved to be solvable. Furthermore, with aid of an integral identity that connects unknown source terms with the known data, a conditional stability is constructed. Theoretical examples are presented showing that theorems and conclusions given in this paper are reasonable and practicable.