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

## 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.

- Authors:

- Universidade Federal da Paraíba, Departamento de Matemática (Brazil)
- Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica (Brazil)
- University of Sevilla, Dpto. EDAN and IMUS (Spain)

- Publication Date:

- OSTI Identifier:
- 22749763

- Resource Type:
- Journal Article

- Journal Name:
- Applied Mathematics and Optimization

- Additional Journal Information:
- Journal Volume: 78; Journal Issue: 2; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; Article Copyright (c) 2017 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0095-4616

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; NAVIER-STOKES EQUATIONS; NONLINEAR PROBLEMS; SOLIDIFICATION

### Citation Formats

```
Araruna, F. D., E-mail: fagner@mat.ufpb.br, Calsavara, B. M. R.,, and Fernández-Cara, E., E-mail: cara@us.es.
```*Local Exact Controllability of Two-Phase Field Solidification Systems with Few Controls*. United States: N. p., 2018.
Web. doi:10.1007/S00245-017-9406-4.

```
Araruna, F. D., E-mail: fagner@mat.ufpb.br, Calsavara, B. M. R.,, & Fernández-Cara, E., E-mail: cara@us.es.
```*Local Exact Controllability of Two-Phase Field Solidification Systems with Few Controls*. United States. doi:10.1007/S00245-017-9406-4.

```
Araruna, F. D., E-mail: fagner@mat.ufpb.br, Calsavara, B. M. R.,, and Fernández-Cara, E., E-mail: cara@us.es. Mon .
"Local Exact Controllability of Two-Phase Field Solidification Systems with Few Controls". United States. doi:10.1007/S00245-017-9406-4.
```

```
@article{osti_22749763,
```

title = {Local Exact Controllability of Two-Phase Field Solidification Systems with Few Controls},

author = {Araruna, F. D., E-mail: fagner@mat.ufpb.br and Calsavara, B. M. R., and Fernández-Cara, E., E-mail: cara@us.es},

abstractNote = {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.},

doi = {10.1007/S00245-017-9406-4},

journal = {Applied Mathematics and Optimization},

issn = {0095-4616},

number = 2,

volume = 78,

place = {United States},

year = {2018},

month = {10}

}

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