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Optimal Control of the Two-Dimensional Vlasov-Maxwell-System

URN to cite this document: urn:nbn:de:bvb:703-epub-3860-2

Title data

Weber, Jörg:
Optimal Control of the Two-Dimensional Vlasov-Maxwell-System.
Bayreuth , 2018 . - 89 P.
(Master's, 2016 , University of Bayreuth, Faculty of Mathematics, Physics and Computer Sciences)

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Abstract

The time evolution of a collisionless plasma is modeled by the Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We only consider a 'two-dimensional' version of the problem since existence of global, classical solutions of the full three-dimensional problem is not known. We add external currents to the system, in applications generated by inductors, to control the plasma in a proper way. After considering global existence of solutions to this system, differentiability of the control-to-state operator is proved. In applications, on the one hand, we want the shape of the plasma to be close to some desired shape. On the other hand, a cost term penalizing the external currents shall be as small as possible. These two aims lead to minimizing some objective function. We prove existence of a minimizer and deduce first order optimality conditions and the adjoint equation.

Further data

Item Type: Master's, Magister, Diploma, or Admission thesis
Keywords: relativistic Vlasov-Maxwell system; optimal control with PDE constraints; nonlinear partial differential equations
Subject classification: Mathematics Subject Classification Code: 49J20, 35Q61, 35Q83, 82D10
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Analysis) > Professorship Applied Mathematics (Applied Analysis) - Univ.-Prof. Dr. Gerhard Rein
Graduate Schools > University of Bayreuth Graduate School
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Analysis)
Graduate Schools
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-3860-2
Date Deposited: 26 Sep 2018 11:43
Last Modified: 26 Sep 2018 11:43
URI: https://epub.uni-bayreuth.de/id/eprint/3860

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