Stable sequential Lagrange principles in the inverse final observation problem for the system of Maxwell equations in the quasistationary magnetic approximation

Abstract

We justify the possibility of using stable, with respect to errors in the input data, algorithms of dual regularization and iterative dual regularization for solving the inverse final observation problem for the system of Maxwell equations in the quasistationary magnetic approximation under general conditions on the coefficients, which is treated as an optimal control problem for the differential equation describing the magnetic field intensity with an operator equality constraint. We state a classical parametric Lagrange principle and stable Lagrange principles in sequential form for the posed problem. We present a stopping rule for the iterative process for the stable sequential Lagrange principle in iterative form in the case of finite fixed error in the input data.