Uniqueness conditions and a method for solving the inverse coefficient problem of heat conduction

A uniqueness theorem in the whole is obtained for the inverse problem of heat conduction involving the definition of the three-dimensional heat-conduction coefficient in terms of temperature changes and measurements of temperature and heat flux density at the boundary. The results can be applied when defining the coefficients of the first spatial derivative and of the distributed heat source. An algorithm for solving the problem is proposed on the basis of iterative regularization, a closure error criterion, and parametrization of the unknown function.