Variational statement of a coefficient inverse problem for a multidimensional parabolic equation

In this paper, we consider the variational statement of an inverse problem of determining the leading coefficient of a multidimensional parabolic equation with nonlocal conditions. The leading coefficient of the equation playing the role of a control function is an element of the Sobolev space. The objective functional is based on the overdetermination condition, which can be interpreted as setting the weighted average value of the solution of the equation considered with respect to the time variable. The well-posedness of the problem in the weak topology of the control space is examined, the Fréchet differentiability of the objective functional is proved, and a necessary optimality condition is obtained.