论文标题
具有动态边界条件的KWC类型的1D抛物线状态系统的最佳控制问题
Optimal control problems for 1D parabolic state-systems of KWC types with dynamic boundary conditions
论文作者
论文摘要
在本文中，我们考虑了一类最佳控制问题，该问题由具有动态边界条件的KWC类型的1D抛物线状态系统控制。状态系统基于晶界运动的相位场模型，该模型在[Kobayashi-Warren，Physica，Physica d，140，141---150，2000]中提出，在上下文中，动态边界条件应该复制多晶体内部和边界之间的传播热交换器。我们的最佳控制问题通过使用常数$ \ varepsilon \ geq 0 $标记，并大致总结了，当$ \ varepsilon = 0 $和$ \ varepsilon> 0 $的情况下，情况分别对应于物理现实的设置，并将其正常设置及其正则化近似。在适当的假设下，数学结果涉及：状态系统的解决性和持续依赖性；最佳控制问题的溶解度和$ \ varepsilon $依赖性；当$ \ varepsilon> 0 $和限制最佳条件为$ \ varepsilon \ downarrow 0 $时，第一阶在问题中的必要最佳条件是;将以本文的三个主要定理形式获得。
In this paper, we consider a class of optimal control problems governed by 1D parabolic state-systems of KWC types with dynamic boundary conditions. The state-systems are based on a phase-field model of grain boundary motion, proposed in [Kobayashi--Warren--Carter, Physica D, 140, 141--150, 2000], and in the context, the dynamic boundary conditions are supposed to reproduce the transmitted heat exchanges between interior and boundary of a polycrystal body. Our optimal control problems are labeled by using a constant $ \varepsilon \geq 0 $, and roughly summarized, the case when $ \varepsilon = 0 $ and the cases when $ \varepsilon > 0 $ correspond to the physically realistic setting, and its regularized approximating ones, respectively. Under suitable assumptions, the mathematical results concerned with: the solvability and continuous dependence for the state-systems; the solvability and $ \varepsilon $-dependence of optimal control problems; and the first order necessary optimality conditions in the problems when $ \varepsilon > 0 $ and the limiting optimality condition as $ \varepsilon \downarrow 0 $; will be obtained in forms of three Main Theorems of this paper.
