Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems
We formulate and study robust control problems for a two-dimensional time-dependent Ginzburg-Landau model with Robin boundary conditions on phase-field parameter, which describes the phase transitions taking place in superconductor films with variable thickness. The objective of such study is to con...
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2006-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA/2006/26724 |
| Summary: | We formulate and study robust control problems for a
two-dimensional time-dependent Ginzburg-Landau model with Robin
boundary conditions on phase-field parameter, which
describes the phase transitions taking place in superconductor
films with variable thickness. The objective of such study is to
control the motion of vortices in the superconductor films by
taking into account the influence of noises in data. Firstly, we
introduce the perturbation problem of the nonlinear governing
coupled system of equations (the deviation from the desired
target). The existence and the uniqueness of the solution of the
perturbation are proved as well as stability under mild
assumptions. Afterwards, the robust control problems are
formulated in the case when the control is in the external
magnetic field and in the case when the control is in the initial
condition of the vector potential. We show the existence of an
optimal solution, and we also find necessary conditions for a
saddle point optimality. |
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| ISSN: | 1085-3375 1687-0409 |