scholarly journals Distributed optimal control of a nonstandard system of phase field equations

2011 ◽  
Vol 24 (4-6) ◽  
pp. 437-459 ◽  
Author(s):  
Pierluigi Colli ◽  
Gianni Gilardi ◽  
Paolo Podio-Guidugli ◽  
Jürgen Sprekels
Keyword(s):  
Optimal Control ◽  
Phase Field ◽  
Field Equations ◽  
Distributed Optimal Control ◽  
Phase Field Equations

scholarly journals State-constrained optimal control of phase-field equations with obstacle

2013 ◽  
Vol 2013 (1) ◽  
pp. 234 ◽  
Author(s):  
Jiashan Zheng ◽  
Junjun Liu ◽  
Hao Liu
Keyword(s):  
Optimal Control ◽  
Phase Field ◽  
Field Equations ◽  
Constrained Optimal Control ◽  
Phase Field Equations

Mixed Control Problem for the Linearized Quasi-Stationary Phase Field System of Equations

2016 ◽  
Vol 845 ◽  
pp. 170-173 ◽  
Author(s):  
Marina Plekhanova
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Phase Field ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Operator Differential Equation ◽  
Field Equations ◽  
Mixed Control ◽  
Phase Field Equations

Conditions are obtained for unique solution existence of a mixed control problem without taking in account control expenses for a system that described by an initial-boundary value problem for the linearized quasi-stationary system of phase field equations. The problem is reduced to an optimal control problem for operator differential equation of first order in abstract space with degenerate operator at derivative using start and distributed controls simultaneously. The theorem on the unique solvability of this problem is applied to studying of optimal control problem for the phase field equations system.

Asymptotic Compactness and Attractors for Phase-Field Equations in ℝ3

2008 ◽  
Vol 16 (7-8) ◽  
pp. 861-897 ◽  
Author(s):  
Francisco Morillas ◽  
José Valero
Keyword(s):  
Phase Field ◽  
Field Equations ◽  
Asymptotic Compactness ◽  
Phase Field Equations

scholarly journals Distributed optimal control of a nonstandard nonlocal phase field system

2016 ◽  
Vol 1 (3) ◽  
pp. 225-260 ◽  
Author(s):  
Pierluigi Colli ◽  
◽  
Gianni Gilardi ◽  
Jürgen Sprekels
Keyword(s):  
Optimal Control ◽  
Phase Field ◽  
Distributed Optimal Control ◽  
Field System ◽  
Phase Field System
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