Existence of solution for an optimal control problem associated to the Ginzburg-Landau system in superconductivity

2019/02/12 by Fabio Botelho, Botelho, Fabio, Eduardo Pandini Barros +1
Engineering · Mathematics · Physics and Astronomy · #49J20 #Control and Stability of Dynamical Systems #FOS: Mathematics #Optimization and Control (math.OC) #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations #math.OC #msc:49J20

paper · pdf · doi:10.48550/arxiv.1902.04448

8 pages

arxiv created 2019/02/12 · openalex publication_date 2019/02/12 · arxiv updated 2019/02/13 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

This article develops a global existence result for the solution of an optimal control problem associated to the Ginzburg-Landau system. This main result is based on standard tools of analysis and functional analysis, such as the Friedrichs Curl Inequality and the Rellich-Kondrashov Theorem. In the concerning model, we consider the presence of an external magnetic field and the control variable is a complex function acting on the super-conducting sample boundary. Finally the state variables are the Ginzburg-Landau order parameter and the magnetic potential, defined on domains properly specified.

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