Uniqueness theorems for the solution of an inverse heat conduction problem

The single-valued conditions of solution of the inverse heat conduction problem are formulated in terms of properties of an observed unsteady temperature field and possible sufficient variations of the initial distribution. A close relationship is found between single-valued conditions and group properties of the heat conduction equation, in particular, there is agreement between a class of temperature fields giving nonsingle-valued solution of the inverse problem and that of invariant solutions.