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 |
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Wiley
2006-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA/2006/26724 |
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| _version_ | 1832567303332429824 |
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| author | Aziz Belmiloudi |
| author_facet | Aziz Belmiloudi |
| author_sort | Aziz Belmiloudi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-484a518306104adda659d90b04070980 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-484a518306104adda659d90b040709802025-02-03T01:01:48ZengWileyAbstract and Applied Analysis1085-33751687-04092006-01-01200610.1155/AAA/2006/2672426724Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systemsAziz Belmiloudi0Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes1, Rennes Cedex 35042, FranceWe 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.http://dx.doi.org/10.1155/AAA/2006/26724 |
| spellingShingle | Aziz Belmiloudi Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems Abstract and Applied Analysis |
| title | Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems |
| title_full | Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems |
| title_fullStr | Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems |
| title_full_unstemmed | Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems |
| title_short | Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems |
| title_sort | robust control problems of vortex dynamics in superconducting films with ginzburg landau complex systems |
| url | http://dx.doi.org/10.1155/AAA/2006/26724 |
| work_keys_str_mv | AT azizbelmiloudi robustcontrolproblemsofvortexdynamicsinsuperconductingfilmswithginzburglandaucomplexsystems |