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Applied Mathematics & Optimization

, Volume 78, Issue 2, pp 267–296 | Cite as

Local Exact Controllability of Two-Phase Field Solidification Systems with Few Controls

  • F. D. Araruna
  • B. M. R. Calsavara
  • E. Fernández-Cara
Article
  • 182 Downloads

Abstract

We analyze a control problem for a phase field system modeling the solidification process of materials that allow two different types of crystallization coupled to a Navier–Stokes system and a nonlinear heat equation, with a reduced number of controls. We prove that this system is locally exactly controllable to suitable trajectories, with controls acting only on the motion and heat equations.

Keywords

Phase field models Solidification models Controllability Observability 

Mathematics Subject Classification

82B26 35K55 93B05 93B07 

Notes

Acknowledgements

This paper was written in part during several visits of the first and second authors to the Institute of Mathematics of the University of Sevilla (IMUS). The authors are indebted to this Institute for its assistance. The authors are also indebted to the anonymous referee for his/her comments and suggestions, that led to essential improvements of the paper. F.D. Araruna was partially supported by INCTMat, CAPES, CNPq (Brazil) and MathAmSud COSIP. B.M.R. Calsavara was partially supported by FAPESP, Grant Nos. 2012/15379-2 and 2014/16802-1, and CNPq (Brazil), Grant No 211473/2013-8. E. Fernández-Cara was partially supported by Grant No MTM2013-41286-P, DGI-MICINN (Spain) and CAPES (Brazil).

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • F. D. Araruna
    • 1
  • B. M. R. Calsavara
    • 2
  • E. Fernández-Cara
    • 3
  1. 1.Departamento de MatemáticaUniversidade Federal da ParaíbaJoão PessoaBrazil
  2. 2.Instituto de Matemática, Estatística e Computação CientíficaUniversidade Estadual de CampinasCampinasBrazil
  3. 3.Dpto. EDAN and IMUSUniversity of SevillaSevillaSpain

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