A boundary control problem for a possibly singular phase field system with dynamic boundary conditions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:434

Article

Colli, Pierluigi^1,2  Gilardi, Gianni^1,2  Marinoschi, Gabriela³ 

[1] Univ Pavia, Dipartimento Matemat F Casorati, I-27100 Pavia, Italy

[2] CNR PAVIA, IMATI, I-27100 Pavia, Italy

[3] Romanian Acad, Gheorghe Mihoc Caius Iacob Inst Math Stat & Appl, Bucharest 050711, Romania

关键词: Phase field system;    Phase transition;    Singular potentials;    Optimal control;    Adjoint state system;    Dynamic boundary conditions;   

DOI  :  10.1016/j.jmaa.2015.09.011

来源: Elsevier

【 摘 要 】

This paper deals with an optimal control problem related to a phase field system of Caginalp type with a dynamic boundary condition for the temperature. The control placed in the dynamic boundary condition acts on a part of the boundary. The analysis carried out in this paper proves the existence of an optimal control for a general class of potentials, possibly singular. The study includes potentials for which the derivatives may not exist, these being replaced by well-defined subdifferentials. Under some stronger assumptions on the structure parameters and on the potentials (namely for the regular and the logarithmic case having single-valued derivatives), the first order necessary optimality conditions are derived and expressed in terms of the boundary trace of the first adjoint variable. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free