In this paper statements in Holder spaces for ill-posed inverse problems with final overdetermination are studied for parabolic equations with unknown coefficients multiplying lower-order terms or lower-order derivatives. Sufficient conditions are found that ensure the uniqueness property for this class of inverse problems using the duality principle. Such approach relates the uniqueness problem considered to uniqueness property for linear backward parabolic operators. Examples of instability and loss of uniqueness are presented

Ключевые слова: Coefficient inverse problems, parabolic equations in Holder spaces, final overdetermination, ill-posed problems, uniqueness property, duality principle, inverse uniqueness for linear backward operators