论文标题
用分数操作员对Caginalp类型的相位场系统的最佳控制
Optimal control of a phase field system of Caginalp type with fractional operators
论文作者
论文摘要
在他们最近的工作中，“分数相位野外系统的体积，规律性和渐近分析”（Asymptot。Anal。114（2019），93-128；另请参见预印度ARXIV：1806.04625），其中两个作者已研究了阶段的两种型号，这些阶段是不相同的，以及不相同的阶段，并构成了不相同的范围，并构成了不相同的范围。运算符是由分数版本以无界，单调，自偏连接，线性算子具有紧凑分辨率的光谱含义给出的。在本文中，我们通过研究此类系统的分布式最佳控制问题来补充这种分析。结果表明，相关的控制对状态运算符在合适的Banach空间之间是可区分的，并且有意义的一阶必要的最佳条件是根据变异不平等和相关的伴随状态变量得出的。
In their recent work `Well-posedness, regularity and asymptotic analyses for a fractional phase field system' (Asymptot. Anal. 114 (2019), 93-128; see also the preprint arXiv:1806.04625), two of the present authors have studied phase field systems of Caginalp type, which model nonconserved, nonisothermal phase transitions and in which the occurring diffusional operators are given by fractional versions in the spectral sense of unbounded, monotone, selfadjoint, linear operators having compact resolvents. In this paper, we complement this analysis by investigating distributed optimal control problems for such systems. It is shown that the associated control-to-state operator is Fréchet differentiable between suitable Banach spaces, and meaningful first-order necessary optimality conditions are derived in terms of a variational inequality and the associated adjoint state variables.
