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This paper is devoted to the study of a class of optimal control problemsgoverned by 1-D Kobayashi-Warren-Carter type systems, which are based on aphase-field model of grain boundary motion, proposed by [Kobayashi et al,Physica D, 140, 141-150, 2000]. The class consists of an optimal controlproblem for a physically realistic state-system of Kobayashi-Warren-Cartertype, and its regularized approximating problems. The results of this paper arestated in three Main Theorems 1-3. The first Main Theorem 1 is concerned withthe solvability and continuous dependence for the state-systems. Meanwhile, thesecond Main Theorem 2 is concerned with the solvability of optimal controlproblems, and some semi-continuous association in the class of our optimalcontrol problems. Finally, in the third Main Theorem 3, we derive the firstorder necessary optimality conditions for optimal controls of the regularizedapproximating problems. By taking the approximating limit, we also derive theoptimality conditions for the optimal controls for the physically realisticproblem.

Optimal Control Problems Governed by 1-D Kobayashi-Warren-Carter Type Systems