Penalization of Dirichlet Boundary Control for Nonstationary Magneto-Hydrodynamics
Pages 2354 - 2382
Abstract
Penalization of Dirichlet boundary controlled nonstationary magneto-hydrodynamic equations is considered. Asymptotic behavior of solutions of a penalized control problem with respect to the penalty parameter is investigated. It is proved that solutions of the penalized boundary control problem converge to the solutions of the Dirichlet control problem as penalty parameter $\epsilon$ goes to zero. The existence of optimal solutions as well as the characterization of such solutions by first order necessary conditions are established. A second order sufficient optimality condition for the optimal control problem is also developed. Numerical results are provided showing the feasibility and effectiveness of the penalty method.
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DOI:10.1137/sjcodc.58.4
Issue’s Table of Contents© 2020, Society for Industrial and Applied Mathematics.
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Society for Industrial and Applied Mathematics
United States
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Published: 01 January 2020
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