Abstract
An optimal control problem with state-space constraints for a multidimensional Stefan problem in an enthalpy formulation with nonlinear boundary conditions is investigated. The existence and stability of a solution of the optimal control problem is shown providing a set of admissible controls is compact. Also, a boundary observation is admitted. The original problem is then approximated by using a penalty-function method, finite-element method in space and backward Euler formula in time. The convergence of the approximate optimal controls is proved. Moreover, an example for non-stability of the penalty-function method inL p spaces is constructed. Finally, numerical results of an illustrative example are presented.
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