Abstract
We study the approximation of unsteady magnetohydrodynamic equations with Dirichlet control by equations with penalized Neumann control. We prove the existence of optimal solutions to the penalized control problem. We prove the convergence of solutions of penalized control problem to the corresponding solutions of the Dirichlet control problem, as the penalty parameter goes to zero. First order order necessary and second order sufficient optimality condition are developed. Numerical results are provided.
Penalization of Dirichlet Optimal Control Problem for Magneto-Hydrodynamics
We study the approximation of unsteady magnetohydrodynamic equations with Dirichlet control by equations with penalized Neumann control. We prove the existence of optimal solutions to the penalized control problem. We prove the convergence of solutions of penalized control problem to the corresponding solutions of the Dirichlet control problem, as the penalty parameter goes to zero. First order order necessary and second order sufficient optimality condition are developed. Numerical results are provided.
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