# Optimal Control and Controllability of a Phase Field System with One Control Force

Optimal Control and Controllability of a Phase Field System with One Control Force We investigate the relation between optimal control and controllability for a phase field system modeling the solidification process of pure materials in the case that only one control force is used. Such system is constituted of one energy balance equation, with a localized control associated to the density of heat sources and sinks to be determined, coupled with a phase field equation with the classical nonlinearity derived from the two-well potential. We prove that this system has a local controllability property and we establish that a sequence of solutions of certain optimal control problems converges to a solution of such controllability problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Optimal Control and Controllability of a Phase Field System with One Control Force

, Volume 70 (3) – Dec 1, 2014
25 pages

/lp/springer_journal/optimal-control-and-controllability-of-a-phase-field-system-with-one-JDpxdOT0yd
Publisher
Springer US
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-014-9249-1
Publisher site
See Article on Publisher Site

### Abstract

We investigate the relation between optimal control and controllability for a phase field system modeling the solidification process of pure materials in the case that only one control force is used. Such system is constituted of one energy balance equation, with a localized control associated to the density of heat sources and sinks to be determined, coupled with a phase field equation with the classical nonlinearity derived from the two-well potential. We prove that this system has a local controllability property and we establish that a sequence of solutions of certain optimal control problems converges to a solution of such controllability problem.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Dec 1, 2014

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