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

• Published in: Differential equations Vol. 52; no. 5; pp. 587 - 603
• Main Authors: Kalinin, A. V., Sumin, M. I., Tyukhtina, A. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.05.2016; Springer Nature B.V
• Subjects: Algorithms; Approximation; Boundary conditions; Difference and Functional Equations; Differential equations; Errors; Inverse; Inverse problems; Lagrange multiplier; Magnetic fields; Mathematical analysis; Mathematical functions; Mathematics; Mathematics and Statistics; Maxwell equation; Optimization techniques; Ordinary Differential Equations; Partial Differential Equations; Principles; Regularization; Regularization methods; Studies
• ISSN: 0012-2661; 1608-3083
• DOI: 10.1134/S0012266116050062

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.