Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems

<p>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...

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Format: Article
Language:English
Published: Hindawi Limited 2006-01-01
Series:Abstract and Applied Analysis
Online Access:http://www.hindawi.com/GetArticle.aspx?doi=10.1155/AAA/2006/26724
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spelling doaj-e386df41dcc8453d95d765d7f324ca5e2020-11-25T01:11:17ZengHindawi LimitedAbstract and Applied Analysis1085-33752006-01-012006Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems<p>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.</p>http://www.hindawi.com/GetArticle.aspx?doi=10.1155/AAA/2006/26724
collection DOAJ
language English
format Article
sources DOAJ
title Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems
spellingShingle Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems
Abstract and Applied Analysis
title_short 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_sort robust control problems of vortex dynamics in superconducting films with ginzburg-landau complex systems
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
publishDate 2006-01-01
description <p>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.</p>
url http://www.hindawi.com/GetArticle.aspx?doi=10.1155/AAA/2006/26724
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