Variational method for solving a coefficient inverse problem for a parabolic equation with integral conditions

In this paper, we consider an inverse control-type problem of determining the minor coefficient of a parabolic equation with an integral boundary-value condition and an additional integral condition. The well-posedness of the problem is examined. The Fréchet differentiability of the target functional based on the additional integral condition is proved and an expression for its gradient is found. A necessary condition for the optimality of control is established.