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| Content Provider | Springer Nature Link |
|---|---|
| Author | Gilardi, Gianni Sprekels, Jürgen Colli, Pierluigi |
| Copyright Year | 2012 |
| Abstract | We investigate a nonstandard phase field model of Cahn-Hilliard type. The model, which was introduced in [16], describes two-species phase segregation and consists of a system of two highly nonlinearly coupled PDEs. It has been studied recently in [5], [6] for the case of homogeneous Neumann boundary conditions. In this paper, we investigate the case that the boundary condition for one of the unknowns of the system is of third kind and nonhomogeneous. For the resulting system, we show well-posedness, and we study optimal boundary control problems. Existence of optimal controls is shown, and the first-order necessary optimality conditions are derived. Owing to the strong nonlinear couplings in the PDE system, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional will be of standard type. |
| Ending Page | 149 |
| Page Count | 31 |
| Starting Page | 119 |
| File Format | |
| ISSN | 14249286 |
| e-ISSN | 14249294 |
| Journal | Milan Journal of Mathematics |
| Issue Number | 1 |
| Volume Number | 80 |
| Language | English |
| Publisher | SP Birkhäuser Verlag Basel |
| Publisher Date | 2012-06-04 |
| Publisher Place | Basel |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | parabolic systems Thermodynamics Analysis first-order necessary optimality conditions optimal boundary control Mathematics Cahn-Hilliard systems Nonlinear phase field systems Problems involving partial differential equations Nonlinear parabolic equations |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
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