| Abstract: |
| This study is based on recent jointwork with S. Moll (University of Valencia, Spain) and H. Watanabe (Oita University, Japan).
In this talk, we consider an optimal control problem governed by a one-dimensional nonlinear parabolic system involving a regularized 1-harmonic type flow, which serves as a model of grain boundary motion. The state system is a one-dimensional simplified version of the three-dimensional phase-field model for grain boundary motion studied in [S. Moll et al., J. Nonlinear Sci., 33, 2023].
The optimal control problem is formulated under a state constraint requiring that the range of the state variable is restricted to the unit sphere, together with a control constraint imposed on the domain of the cost functional. In particular, the state constraint introduces essential analytical difficulties in both the mathematical model and the optimal control problem.
The aim of this talk is to lay the foundation for the development of an optimal control framework for our state system. The analysis is built upon a recent uniqueness result for the one-dimensional state system. Under suitable assumptions, we focus on the existence of optimal controls and the corresponding necessary optimality conditions. |
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