Optimal velocity control of a Brinkman-Cahn-Hilliard system with curvature effects
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911363653173248 |
|---|---|
| author | Colli, Pierluigi Gilardi, Gianni Signori, Andrea Sprekels, Jürgen |
| author_facet | Colli, Pierluigi Gilardi, Gianni Signori, Andrea Sprekels, Jürgen |
| contents | We address an optimal control problem governed by a system coupling a Brinkman-type momentum equation for the velocity field with a sixth-order Cahn-Hilliard equation for the phase variable, incorporating curvature effects in the free energy. The control acts as a distributed velocity control, allowing for the manipulation of the flow field and, consequently, the phase separation dynamics. We establish the existence of optimal controls, prove the Fréchet differentiability of the control-to-state operator, and derive first-order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables. We also discuss the aspect of sparsity. Beyond its analytical novelty, this work provides a rigorous control framework for Brinkman-Cahn-Hilliard systems incorporating a curvature regularization, offering a foundation for applications in microfluidic design and controlled pattern formation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05820 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal velocity control of a Brinkman-Cahn-Hilliard system with curvature effects Colli, Pierluigi Gilardi, Gianni Signori, Andrea Sprekels, Jürgen Optimization and Control 35Q35, 35M33, 49K20, 76D07 We address an optimal control problem governed by a system coupling a Brinkman-type momentum equation for the velocity field with a sixth-order Cahn-Hilliard equation for the phase variable, incorporating curvature effects in the free energy. The control acts as a distributed velocity control, allowing for the manipulation of the flow field and, consequently, the phase separation dynamics. We establish the existence of optimal controls, prove the Fréchet differentiability of the control-to-state operator, and derive first-order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables. We also discuss the aspect of sparsity. Beyond its analytical novelty, this work provides a rigorous control framework for Brinkman-Cahn-Hilliard systems incorporating a curvature regularization, offering a foundation for applications in microfluidic design and controlled pattern formation. |
| title | Optimal velocity control of a Brinkman-Cahn-Hilliard system with curvature effects |
| topic | Optimization and Control 35Q35, 35M33, 49K20, 76D07 |
| url | https://arxiv.org/abs/2601.05820 |