Gol’dman N. L. Inverse problems with final overdetermination for parabolic equations with unknown coefficients multiplying the highest derivative // Doklady Mathematics. 2011. V.83, № 3. 316-320.
This paper deals with coefficient inverse problems in Holder spaces for parabolic equations with additional information specified as final overdetermination. Statements of such problems are studied for sought coefficients with different forms of dependence on space variable and temperature. Sufficient conditions are found that ensure the uniqueness property for this class of inverse problems using the duality principle. Such an approach relates the uniqueness problem considered to uniqueness property for linear backward parabolic operators.
Coefficient inverse problems, parabolic equations in Holder spaces, final overdetermination, uniqueness problem, duality principle, inverse uniqueness