In this article, we consider a class of optimal control problems governed by state equations of Kobayashi-Warren-Carter-type. The control is given by physical temperature. The focus is on problems in dimensions less than or equal to 4. The results are divided into four Main Theorems, concerned with: solvability and parameter dependence of state equations and optimal control problems; the first-order necessary optimality conditions for these regularized optimal control problems. Subsequently, we derive the limiting systems and optimality conditions and study their well-posedness.

中文翻译：

---

由晶界运动的 PDE 模型控制的约束优化问题

在本文中，我们考虑一类由 Kobayashi-Warren-Carter 型状态方程控制的最优控制问题。控制由物理温度给出。重点是维度小于或等于4的问题。结果分为四个主要定理，涉及：状态方程的可解性和参数依赖性以及最优控制问题；这些正则化最优控制问题的一阶必要最优性条件。随后，我们推导了限制系统和最优条件，并研究了它们的适定性。