2020/05/25 by Pierluigi Colli, Colli, Pierluigi, Gianni Gilardi +3
Computer Science · Materials Science · Mathematics · #35K45 #35K90 #35R11 #40J05 #49J20 #49K20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Solidification and crystal growth phenomena
paper · pdf · doi:10.48550/arxiv.2005.11948
openalex publication_date 2020/05/25 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In their recent work `Well-posedness, regularity and asymptotic analyses for\na fractional phase field system' (Asymptot. Anal. 114 (2019), 93-128; see also\nthe preprint arXiv:1806.04625), two of the present authors have studied phase\nfield systems of Caginalp type, which model nonconserved, nonisothermal phase\ntransitions and in which the occurring diffusional operators are given by\nfractional versions in the spectral sense of unbounded, monotone, selfadjoint,\nlinear operators having compact resolvents. In this paper, we complement this\nanalysis by investigating distributed optimal control problems for such\nsystems. It is shown that the associated control-to-state operator is Fr 'echet\ndifferentiable between suitable Banach spaces, and meaningful first-order\nnecessary optimality conditions are derived in terms of a variational\ninequality and the associated adjoint state variables.\n