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

Lp‐estimates for scalar products of vector fields and their application to electromagnetic theory problems

“…Let H ∈ L 2,loc (0, ∞, V( )) be a solution of (18), (19), (20). We denote by H c ∈ V( ) a solution of the corresponding stationary problem (12), (13). Proof.…”

“…8,9 The need to design and justification of efficient numerical methods for solving problems has led to the fact that the well-posedness of different mathematical formulations of initial-boundary value problems for the time-dependent eddy current Maxwell's equations currently quite actively studied. [10][11][12][13][14] The present work deals with the formulation of time-dependent eddy current problem in unbounded heterogeneous domain in terms of magnetic field. Using the inequalities for scalar products of vector fields, we study the issues of correctness of the problem and properties of solutions, in particular, their stabilization as t → ∞.…”

“…For any J ext ∈ {L 2 (R 3 )} 3 such that J ext I ∈ K(Ω J ), there exists a unique solution H ∈ V( ) of the problem(12),(13).…”

Regularization of Pontryagin Maximum Principle in Optimal Control of Distributed Systems

“…Thus, they contribute to a significant expansion of the range of applicability of the theory of optimal control in which a central role belongs to classic constructions of the Lagrange and Hamilton-Pontryagin functions. Finally, we note that discussed in this paper regularized Lagrange principle in the nondifferential form and Pontryagin maximum principle may have another kind, more convenient for applications [4,9,15]. Justification of these alternative forms of the regularized Lagrange principle and Pontryagin maximum principle is based on the so-called method of iterative dual regularization [11,12].…”