Approximate Solving of an Inverse Problem for a Parabolic Equation with Nonlocal Data

We consider an optimal control problem for the heat conductivity equation with an integral boundary condition. In addition to the instability of the problem in standard function spaces, it is necessary to take into account that the operator of the problem is not self-adjoint To obtain stable (regularized) solutions to the problem posed, we propose to solve a close stable problem with a small parameter in the overdetermination conditions. For the constructed approximate solution, an exact estimate of its deviation from the accurate solution is derived.