This paper deals with coefficient inverse problems in Holder spaces for quasilinear parabolic equations with additional information specified as final overdetermination. The sought function is a coefficient multiplying the time derivative. On the base of the duality principle sufficient conditions are found that ensure the uniqueness property for this class of inverse problems. Examples of admissible solutions are presented. For constructing approximate solutions stable in these Holder spaces the quasisolution method is established.

Ключевые слова: Coefficient inverse problems, parabolic equations in Holder spaces, final observation, ill-posed problems, uniqueness property, duality principle, quasisolution method